{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img style=\"border:0px solid grey;\" src=\"http://hilpisch.com/python_for_finance.png\" alt=\"Python for Finance\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Buy the book ** |\n",
    "<a href='http://shop.oreilly.com/product/0636920032441.do' target='_blank'>O'Reilly</a> |\n",
    "<a href='http://www.amazon.com/Yves-Hilpisch/e/B00JCYHHJM' target='_blank'>Amazon</a>\n",
    "\n",
    "**All book codes & IPYNBs** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**The Python Quants GmbH** | <a href='http://pythonquants.com' target='_blank'>www.pythonquants.com</a>\n",
    "\n",
    "**Contact us** | <a href='mailto:analytics@pythonquants.com'>analytics@pythonquants.com</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical Tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "uuid": "460b709e-eed1-48e4-b3ad-d07377ea5de6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "uuid": "2326c3ad-f244-4f48-8b68-851bd2347d57"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "uuid": "c09f73d2-c2a5-4c6d-a2f1-08a191378417"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "uuid": "96d2bd1b-8883-486d-920d-b610aeb076a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188fd70210>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hv/61jvpFpDpEH+ffnrz1/EVEUqC5fUREpCQV/wyk0gdUzmylkDOFjKCcMaj4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\nIlKDVPxFRGqQir+ISA36f1jF9Jt3Z5JXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188fda4fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b')\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot\n",
    "# title: Example function plot\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monomials as Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "uuid": "ace90420-7219-4227-8210-bf107f556726"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=1)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "uuid": "c0667d3e-a48a-413d-b250-5e0d3b58275e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188fd63510>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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31Y/1/AMQlT5gKHMmOUkrUzkfewwaNYIrr6zY80O5PYuJQkawnD6kbc9fRKYB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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188fca5310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_1\n",
    "# title: Example function and linear regression\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "uuid": "096bb07a-55f7-45de-8734-2a76d8749d53"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=5)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "uuid": "5e17309e-e8e2-4df9-b841-0f57d983b89e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188fd70fd0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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S2+9rUzab2iKeto+T0T6q+il4AY1JmZyc/VV+8mT2HB7i+uvhd7+zwm/qHuv5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\nir8xxtRBVvyNMaYO+n9PB1bjXlWXeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188fba0590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_2\n",
    "# title: Regression with monomials up to order 5\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "uuid": "67b14a21-e8f2-4dd4-a43b-0d232f2b4055"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), 7)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "uuid": "053752b7-7eb3-4d93-acdf-69874ceada12"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188fafc2d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nbNsGQ4fCs89Co0Y1e64g7M8gZATL6YKTI39VfQt4y8Vr1wmRCESj3qrj+bYK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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188fb4fe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_3\n",
    "# title: Regression with monomials up to order 7\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "uuid": "e600b6be-4cf2-4212-807a-7f397f081e98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "uuid": "bc6918fe-f520-483c-94eb-41dd89abfa70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017769134759517413"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Individual Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "uuid": "b4f05890-56e0-4f29-9d61-bd9948ad8af0"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((3 + 1, len(x)))\n",
    "matrix[3, :] = x ** 3\n",
    "matrix[2, :] = x ** 2\n",
    "matrix[1, :] = x\n",
    "matrix[0, :] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "uuid": "c8963eee-4bc8-4ef2-a172-d4b64fd065a3"
   },
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "uuid": "efd077d1-9c8a-4961-be95-400f83cd679e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.13968447e-14,   5.62777448e-01,  -8.88178420e-16,\n",
       "        -5.43553615e-03])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "uuid": "efb7b252-d0f8-4263-b2be-4d9588ab06a7"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "uuid": "1b1953fe-83a2-436b-8cd4-69c5abf6d2e1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188fa58690>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Izc0FICcnh7y8vJJLvhV/EL6Xi4UlT7Ll4mvuhiWPbc/0LxcWFoYqT8rLAwa4g6sHH0z+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\nir8xxmQhK/7GGJOF/h/yUfa68o5vDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188f9f5810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_4\n",
    "# title: Regression via least-squares function\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "uuid": "ac77ef01-8abe-4b99-8f92-8325a396ff2c"
   },
   "outputs": [],
   "source": [
    "matrix[3, :] = np.sin(x)\n",
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]\n",
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "uuid": "58d9db31-5885-4fba-8ae7-2e962a0963ca"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188f9e03d0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bB/Lz4aST4O67XScxJvGCMp9/nQGNSbTXXvPO0PXss66TGOOOq6GeF4vIKqA/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\nJg1Z8TfGmDRkxd8YY9KQFX9jjElD/w981KJx0nucaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188f88cc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_5\n",
    "# title: Regression using individual functions\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "uuid": "02481bd5-c737-46bc-9b90-5554fcad8745"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "uuid": "6bf80137-3a52-483b-a557-b092bbf23b36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2749084503102031e-31"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "uuid": "86f9a92c-600d-4515-b34d-20c9f35a86b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.55428020e-16,   5.00000000e-01,   0.00000000e+00,\n",
       "         1.00000000e+00])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "uuid": "75d3a6a6-a940-4a49-b35d-29f21880ab95"
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-2 * np.pi, 2 * np.pi, 50)\n",
    "xn = xn + 0.15 * np.random.standard_normal(len(xn))\n",
    "yn = f(xn) + 0.25 * np.random.standard_normal(len(xn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "uuid": "f6f9c05f-1f96-48ee-aaca-f4d80c3d3ac5"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xn, yn, 7)\n",
    "ry = np.polyval(reg, xn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "uuid": "9a475222-3bfd-4300-951b-94e60792c6da"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188f836350>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oAx6LwWufBnzYaHmvb53jOKUOqDmj452y2YV3quYc5s5daHWkVtl1XwbTnPHX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\npaRQn5zMZb6J2Pw5b7rpXnb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188fa90d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xn, yn, 'b^', label='f(x)')\n",
    "plt.plot(xn, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_6\n",
    "# title: Regression with noisy data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unsorted Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "uuid": "8ea85cdb-47f2-4967-b684-7894d9964e76"
   },
   "outputs": [],
   "source": [
    "xu = np.random.rand(50) * 4 * np.pi - 2 * np.pi\n",
    "yu = f(xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "uuid": "0034edf5-1cef-4eea-be44-c69103fe6eb2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.22  4.42  2.61  5.37 -4.4  -4.1  -2.64  1.84 -5.12  5.09]\n",
      "[ 1.74  1.25  1.81  1.89 -1.25 -1.23 -1.8   1.88 -1.64  1.61]\n"
     ]
    }
   ],
   "source": [
    "print xu[:10].round(2)\n",
    "print yu[:10].round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "uuid": "d7f5f003-1cb8-4432-a8d6-cb4bef1a101a"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xu, yu, 5)\n",
    "ry = np.polyval(reg, xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "uuid": "40177962-0363-479c-bdbd-451a4c043060"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188f719450>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Qzfnbyp49cyZz09ObbCtIT+eCGGr3uPm1B8vvBq2O/EWkEPhvVf2y+W2qWisi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\nOGTF3xhj4pAVf2OMiUNW/I0xJg79f/OIkpmQOW9BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188f72f8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xu, yu, 'b^', label='f(x)')\n",
    "plt.plot(xu, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_7\n",
    "# title: Regression with unsorted data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "uuid": "82b95a7b-9e3e-4dc8-b313-1af775b06b8b"
   },
   "outputs": [],
   "source": [
    "def fm((x, y)):\n",
    "    return np.sin(x) + 0.25 * x + np.sqrt(y) + 0.05 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "uuid": "b03b67ac-f7df-41d1-9dab-1e074e8738fa"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10, 20)\n",
    "y = np.linspace(0, 10, 20)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "  # generates 2-d grids out of the 1-d arrays\n",
    "Z = fm((X, Y))\n",
    "x = X.flatten()\n",
    "y = Y.flatten()\n",
    "  # yields 1-d arrays from the 2-d grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x7f188f46d998>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WtCMGNKuFFpWj8d76fRhaNQbtnNQNf5yjRlTpMJQNcd+cJCGyFGaHh+DrWVNQ\nrmErDHxnRFAWoQGAc6cTseG7rzGwQghq1o+z/v3bk8noVtZxfF1nNuPHJ8/wnEehbcVy+KHaC5AI\n/r32aqMROp0R8XLuGodozWaYKQqVQ/Jc74ub1MCup5mYeS8VHTUiNBVy0zSGpmlYJBT6Zz/Hx717\nYchnn6FJi5ZejWGxWIJyV0ZRwZcGwbXQcT/kf3qftLNOVZ5aomq1GkKhEGKxf+3wnGEymaDT6aBU\nul/Fs4lhbPcpT4qoBKoVpqsOWyaTydrNSi6Xe5z08nqHNqBMenwx+HXUrRTj0TG/Hj4NXXo6hjbj\npqBEn+XbsH5kD59EmsVktmDatuPIzczGjJa1Crz+kfuSMLtnG8SU8s5yS36Sjl+vp6FR51fRvc+b\n+cZlvUOB+py6Ii0tDT/Nn40KuU/xZrVo8Hj5v0d9f96D+VViC3y/1qU+xzWLCSPrV0XDcuEOx/74\n0AW8Fqr0Kpbtjtm37qNPpSjUCM1v2RotNH65n4azTzLQXy9FnMC/PeebLTmoHheOF0NDwDAM/tQa\nwGveCu9/9rnThZZ9N7OcnBwMHz4cu3fv9msuhUDA3TgURTH7Y7gtHOMLnR5f5tzd/Z9NC3TVqSo7\nOxuAZ52qitqSZt3xKpXKaj17I7qFZUmzxSvUajVkMhlCQkI8Fujz586iZkwZ/D71XY8FGgC2HDmL\ngY1r+jrlfPhjRdsiFPDxZc+26NaiLgbvPosnKo31secaHUIVMq8FGgBqR5fB7Pa1EHXrJD55ZxAO\n7NlVpK7Qa1ev4ov3/4d1H4/B8FIm9K8eU0CgV569jo7hYfm+X1dzcjH+3kNUii+Hn7o0cSrQerMZ\nmbk6TgXaSNNQ0UwBgQYAEZ+Ht+OjMLdJAk5E87GAlwUVbfb5XDdENFor885DURS6yyV44cwJfNC7\nF+7dvevRGGq1mvN2sMUZnoAq8p9AEJy+sQBimxjGWs5sOU82u9jR3lxHBDrO506kvY3pOho/UNjO\nm3XBC4VCn+qY/7ZqOWYM7OqVQK7afxJda8cXWSzaHR1rVkLd8hH4cP0+vBihRL+acZh+6iqmdGvt\n17gt4qLQvGI57Dm+DZM2bUCvt0eiXsNGHM3aNQzD4NihQ9i7YQ2qQIcPq0ZBEuc81rznSgrmVc57\nXGc2Y+6jp4guE4ofujSG3E0oY+aJK+gfzV0sGgAW33uMgZXKuXxOqEiIT2rG4YFGh+9vPoIkR4O3\naM8XnAD77gh8AAAgAElEQVRw0JSLNuXCCnz/4iVijKL1WP7uO6jxRl8MGD6iQDa3fUlQUsjkX/jS\nkmlzlsxX5QBWnA0GQz6BBvL2aqpUKohEIiiVSo8t0aKM6Wq1WuTm5kIikSAkJMTn2FSgsruBPG+F\nWq2GVquFXC73yr3Ncj7pHGqXlnptwW7/KwkDGtfw6hhnrD19GV09yOj2lrJKOdaM6A5diBLv7j0L\nvlCE+DL+Fc8A8q7/y9UrYE7rakjZvAKfjx2F61evcjBjx5hMJvy2ZhU+GdoPuX+uxGfVS2NgzQqQ\nCJ3bAFsv30WLUCX4FIUNT59jRuozjGv5Aj5tXtOtQJtpGo+z1Kit5M6KNNM00kxm1PfQixErl2Ju\n/ap4qXZ5fCnMxjOz0eNzJUpMeCXc8fss4vEwVC4Gf9MGTBgyKF+lMtIByzUUnyrynwJzoqiVFEWl\nURSVbPO3cIqi9lMUdZOiqH0URbn80v8nRNrWtQ3A2ruWLTtJ0zRCQ0O93kNcFIlj9nP2Z592oCxp\ntodwTk4OeDye1y54Wzau/Al9vKy1/f22w+jTsDr4HG2d2Z58F4OaBybeRVEUxnZsDJ5UgsdaPS4+\neMrZ2Dwehb514zG9aUWc+3kRxg4diN3btyEtLY2T8VUqFb6fPwfTh/VH3JWjmF4vBi9VKlfAre2I\n9Um3UF3Ex/h7DxETF4HlLzdBtXDPBGfOqSvoy7EV/dP9VPSNc21FO6JlaSXmN0nAr2EG7KPVbp+f\nZNKgYXgoBG6uUSOZBP0y0vDFm32wb8cOa+Eh2/sBKQmaH76QV+Q/DvgZQBe7v00CsJ9hmGoADv7z\nu1NKtLvb2Z5nX5KsXJ2jMLAtlenvnAMJGzYA4HfLy7NnzqBuhMwrC5amaRxOuowNb3fz+by2LDt+\nEb2b1OJM8B2h0uohkSmwZcI7mLRiC3Zff4hPXmrM2fgiAR+D68dj+IaDiLx+FH8e2oo0PQ1I5VCW\njUKDFq1Rr0EDp1aZwWBASkoKbl27ittXL0ObnYnHjx5C+zwNU1vUQIUG3hXlOHTrAZ7kqHCsbBiW\ndmkMhRetRmmaxu1nKoysyV3PZpqmcVdvwPvhvm2zKiUWYUHDBKy5n4YFD9LxnjkUIieflz1iA2aW\n8WwxoBQKMEbA4Ic5MxEdF4e4uDgAeYujH374AQqFwutkwGHDhmHnzp2IiIhAcnKecZeZmYm+ffvi\n/v37iIuLw2+//eYw6TPYoTgKbXEJwzDHKYqKs/vzawDa/PP/1QCOwIVQl8jsbjZr22w2O9zzzFX1\nLb1ebxXNQMAwDLKysiCTyaDT6SAWizlr3gHAmmXNRXckhmFgMBis89Tr9QgPd5z04ykTR7+DWd1b\ngu/Fl2/eb3tQQynBK7Vc7xv2BJqm0W/lDmwY1TOgpRf/t24vxvTujFoV85Lifjt+HhsPnMDSXm0Q\nzlFi1JRtx9GtUU20qFI+39+ztTqcv5+GC09zoIYAjFgOZZkI5GZngTLqAKMeItqE+FJyVC2tQJXI\n0giRitFv8e/4qmMDhLsoIuOINRdvYeWpZCzq3Aw1S3svigtOX0M1hofmPiTXOePn+6lIKKNE2wj/\nS61eV2mwIPku3tRKUVWYf2vYbZMOFyL5GOmlF2AJI8TXW/+EwWAARVHQaDSYN28eTp06hStXrqBa\ntWpo2rQpOnTogH79+rkc6/jx41AoFBg8eLBVpCdOnIgyZcpg4sSJmDt3LrKysjBnzhzvXrhrCiW7\nO7FZk0Cfxi3NEs8UyO7+R6S3MwxT+5/fsxiGKfXP/ykAmezvjihxljRba1ulUkEikVgbSdhu/fEl\nycoRgXZ3sx4Atu1jsO6BtbWelUoleDyetba5r5xOTET9SIVXAk3TNM5dvY0Ph73q17lZFh85jwEt\n6wRUoNV6AwzgWQUaAPq0boDm1eMweulGDKhTCd3qVPHrHDRN4362uoBAA0CYTIr2NeLQ3iZ8r9Lp\nEVI12uli8N7zLETJJV4J9J2MHHzx12VUKlcaXapX8kmgaZrGpScZGFzDdQEbb0nWaDGihnfeAGdU\nV8rxbdOamHvtPs5l5KIf/vVO/C7S4dOyFbwa76pWh2b9+1jfCx6Ph/DwcMyZMwcrV66EVCpFw4YN\nkZiYiMePH7sdr3Xr1khJScn3t23btuHo0aMAgCFDhqBt27Zci3ShwHMQEw52GIZh3FVLC867vo+w\nDRpsEyzYcp5msxkymQxCoZAzSzRQIm1b7AOAV9uVvMHf+dt6JqRSqTU+zo7pqEKSp2xesxyzuntX\n3GHa2h0Y0bouJ+8vTdM4dS8VY7s093ssV0zechTjenYq8PcKZcOxccq7mPPbHuzddATf9nzR58/A\n3P1n8Fbr+h4/Xyl1Lb6fbT6Maa08i9HTNI3Jhy4AUimWj+yNEUt+x8JWvrUL/S7pJnpEleU0l2Lj\nozR0LR/B6ZhSAR9f1I7HzqcZmHUrFWNNIdDQNKLCpQj1Mkx1VCTDvIGDHD6m1WoRHR2Nhg0bomHD\nhj7PNy0tDZGRkQCAyMhIznIWChuesPCLmZzLykFSdo63h6VRFFWOYZinFEVFAXjm6snB58T3A9at\nzd7M2CQrNnkpEOUxuRZp+8SwYCjn6Aiz2QyVSmXtoW0bOvB3zqdOnkDDckqvrGij0YybKQ/Rrho3\nFtG8/WcwrE39gF5/rd4ILUOhdqWCFi4A8Pk8TOn3CgZ3a4/eq3bjZlqG1+dgrc+ONeP8nG0ez1Rq\nhPB5iPIgs3rXjQcYvP0U+nVoju+GdsP951moGiLzKgbNQtM0zj9KR0svG5W4I1GlRmcne7H9pWu5\n0vi0QRUslqmxkE7HwAjvznNfp0dC+w5WD5r9ojc3N5fz7O7iXAuc4lGF/tO4dBhGVq5o/fGQbQCG\n/PP/IQC2unpyiRJpIO9DxiaLmc1mhISEQCaTBeSDx+WYttuVZDIZFAqFdbERKJe6L5Y0W5SE3f6l\nUCg4L034xy8r0atZba+OmbJ6C95r57s1YQtN07j0OB2davof13bF5D+O4oOezmt0s7SoEY9fPhmO\nr09dxzdHLnh1jh+OX8SbzWtz9ln95LcDGNPYdY3k52othm07hQeUCL+PG4AW1fJcvDM3HcC7teN8\nOm8grOhNj9PwckwEeAEUpRi5BDPqVYFeRGHl8wyv+sPvo4QYNHKU9Xf77ypX+6QjIyPx9GneroLU\n1FRERHCbOV9YFHVmt6Psboqi1gM4CSCBoqiHFEW9BWAOgE4URd0E0P6f351SotzdQJ4LSK/XQyAQ\ngM/nBzSOy1UrSduEK3vrOZhWtWxc35u64N7O/+SJv9A4JtQrK1pnMCI1LQNNuzS1/i1XZ8CZe49x\n4dEz3MvWIlOft4+1engI+jWujmqRzrsuTdt5EqPaNwq4FZ1LA3WcWNH2hMplWDZuMNYfOYc+a/Zi\nWIMq6PJCZbfHHbv7BBs6c+OyV2n1gMmCSi6yoOf+lYyHBgsWDO2G8qX/bfV49WEa4mQShLppLuII\n1oruz3Es+kS2Gt9V9ez6+8PCW4+wtGsLZBnMmJB4FaPLhKOywrUn4rnBiIjGzSGT5U8ctC9mwoUl\n/dprr2H16tX4+OOPsXr1anTv3t3vMYsCKgj7ajMM4yyTz/3q/B9KnEiztbQNBkPAt0f5K9Ke9FAO\nZHIa24LTHfZxfTYZLxBsWbMSc3t7XnXLaDTjtc8WgwIweP3BvKx9sQhKuRTVKkSjVdsEDIyKQLnw\nUNAMg4s3U7D1/BXcTbyJHFUuYuRi9KoTj2aVy+ftnTebcTcjBy8mcOM2d8bkrUfxfo8OXh1DURT6\nt2uMXi3rYemuY+i7Zi/Gt66NxpWiHT7/l9OX0a1BDc7yGSb/fhCjHVjRNE1j6dnrSEzLxrD2TTC9\nfsHnTNu4DzOb+tal6NsAWNGbH6ehc0zZgFrRQF7DDggFqFoqT0x/fLkJPj95GaWfajCsnHOLdRdN\n4cNxH+b7m6NiJt5a0v369cPRo0eRnp6OChUqYPr06Zg0aRL69OmDFStWWLdgFUec7FMu9pQ4kRaJ\nRKBp2mMB8hdfBNQ2Mcw24SrYYLuDaTQaiESigMfIjxw8iNZxpT0SlWfZKkxeuxM5RgZly4bj509G\nQeSiwhWQF9tpVKMyGtXIs0AZhsHNh09wMOkq1u44g5xcNR48TsXHr7bi4uU4RW80QWViUC/eu0xf\nFrFIiA+6d8DbL7XE11sOYNFflzHtpUaoEpk/5rnj6n3OSpnqjSaocjWoabNNSW0wYubxZGSYGfRr\nVQ/j+1d1+N7dTn2OcmIBSku9b/BB0zQuPErHAI6t6L9y1PjWQbY71yy48QAjGvzbRzxELMTX7epj\ny+0nmHj5HqZEl0OoXYw+12yGqHpNt1sYfbGk169f7/DvBw4c8GqcYITyoIhOcaTEibRt8lJhWNLe\nYrsVzJM61oG2pJ2NbVs8xdNa5p6O7QiGYbB9wxrM79vO5fP+vvsQs7ccRumISLw/+l0s+PFnTHnz\ndbcC7WyOCbExSIjN2/6k1esxeNYP2H33OXZfTcGC3u08aofpLZP/OIqxPTz2djklRCbB5wNfRXpO\nLub8thdpB5Mwt2sLRITKsfXiTXSsFc9ZKdPP/ziCd/4Rm3sZOZiTeA0yhRyjXm6N+nGO226yfLph\nH6Y1cO+ad0QgrOgtT57hpZiy4Af4pm600MilKLxQNrTAYz2rRKNpZBg+PXYJbSVSdCr97+Jnl8GM\nYRMmFjjGUe1uTzrk/VfgCYKgVWUAKHEizVJYIu3pOXx1GRd2fXD7GLlCoSgUK3/3ju3oUiPG6bm2\nJ/6NVccuomb1BHw17ROEh4Xi4ZOnUAp5qBLjfTlHR0xYsh6fD38TL8TH4tKtFLzzyxYklJJhyist\nOHMZ640mZBktaFDFNyvaEWVCQ/DV8N548CwDMzbshkWnwzOVGutH9uRkfJqm8TAtE/rIMAzddhJV\nYiIxd/CriAkvKD72PEzPRmkehbI+9HwOlBV9LDsX31X2vJuar3x76yHeruN87jEhMix/pSkWX7iD\n6Q+fYHJMOVgYQFshDuXL57fyHd0DDAZDQENPxQ1iSRdDCrMNozNxYfdua7XaQnEZe4P9AsCTGHkg\noGkah7Ztwry+7Qs89u22wzh28xHatmiKZV9Nh8SmDOJnX32HRaPe5GQO6dkqmAG8EJ8Xi65TNQ5r\np3+IvYkX0WfFLnR/oSIGNvcu49wRk7YcwbheBfdFc0FsRGksHTsQy3YexR8nL2LkxkMw6PWoFVEK\nvRpVR/Xosl6Np9UbcfLWfSzamwgzzeAazcfP/+sDhcRzt/Un63Zhch3fsuS/TbrBuRX955Pn6BRV\nJuBWNE3TSDWb0djN9i4eRWFsgyq4VKEsJp28jFihGKPnfO30+fbXIljuJcEAsaSLCVzt1fXmXM5E\nmgvRKwxL2llREn/wZt5bftuI7nXi853zwu0H+Pz3A+jX41WsGjWqgCWbfP0mqkSWRjkn3YS8ZfzS\n9fh8eN8Cf+/crB46Nq6NVTuPoPdP2zGubR20rObxfsh8qPUGqC3wORbtKXsuXMemLz+AVCyC3mjE\nxVsPsO3SDXx78ipUuVqIKAYt4iLQs1FNKCQiJN56iNP3nuBmugq5RjNkUilkEjEUMgmqx0aDLxJh\n+0eDvK5fnpqpgoJhEBXifWnTvIzuDAyoEY80nR43czW4p9EhjQEyaQtoioJYJIJYKICZoaHTGlBb\nwEe3qLJQughRHM5S4bvK1b2ej7f8cOcxBr7g+eKkTtlQ/PRyE3xw7j5q1HJf7MWfQkElFZI4Vswo\nLDexoy9KIEQvELDJdSqVyuee1P5iNptx+sBuzOvXwfr7Byu2QqgMx/KvpkMhc3yDn79kBZZ/NIyT\nOdxLTUOpUAXiohxn2/L5fLz9Wgf0e6kVFm7YgcXHdmDW6y1Rqax3tZ4nbjqMj96wb4jDLUf/voEm\nNatAKs5zg0pEIjSrVQXNav1bWjQ9Jxenr93FghPXYDSZUb1iNFq1bIqh5cuhbFhIvs/qgg07MbJT\nc58ajHy8dicm1vXeit5y4wF++PsW4kuF4tscFUrJxKgYF4lWIVJEhUgRGSJDiDi/m1drNCPx4TOs\nu5eKtOeZMOgMqCcSolt0Wcj+WRxve/IMHWMKx4q+qTPg4xjvmoAcTM3CuC9mOHzMkSgToc5PMG7B\n4gIi0hyfh+sa4YEsPWowGKwNQoqqGtv6NavwZpO8hKR9SVfw/f4z+HDEUDSu69yaOJp4Fo0TKiGU\no+YTk3/6HQs/dC/4MokYU4b2wrOsHExdug61SknxfkfPulVla3Uw8wX5anQHgu92HMWqSSNcPqdM\naAi6NquLrs3qunweTdM4k3wDH71X0MPgjscZ2ZDTNGJCPGs+k6nV46vzt5HD46FznaqIffgcK3u3\n8fgzKRMJ0L5yNNpXztuOlmsw4uSDZ1h59ymeq3Uw6Qx4qlJjlZdtT31hbUoq3qhR0avvE8MwuGiR\noH+LFk4fJ4LsGp6gZIp0iXtVhZndbXseNhtao9FYK4YFaxMPk8lkLT3K4/ECYul7Mp7RaMTlU0dR\nPSYSgxetw8mnWqxZNNulQAPA8rW/Y6yDete+cOHmPVSJjUakF27ziFKh+GnyaIRVrIT+K7ZD+0+h\nFFdM2nwEE97o7M9U3XLyym00TIiH3IetTo5YsvUA+rXwrRb6pLW7Maau+4SvwympGHH4IhbdScPo\n7m2xbnRv3H2ageGNq/v1mQwRi9C5annM7twIy3u1RuuEaFSILIUPr9zD3xnZPo/rCUm5OnSOi/Tq\nmAOPMvDyoLc8fr7JZAradrVFBcXjFfmPw3lR1PsURSVTFHWZoqj3vX1dxJL2EzYxjM20DKbEMHto\nmoZOp4PRaIRcLgePx7N2ryoKVi//EXLGiMHf/46p77+LapXcFxD5fed+dGlSGxKOslpnr9uOnyaP\ncv9EBwx5pS1a1E7AwG9XYVybOmid4DhWnZ6rAU8sQUJ5brLQnbFw62GsnPQOZ+MdS7qM33y0ohUM\njWgnsWit0YxvLt5Cit6CNrXisXJUK2symtlsxvWHqfi4cVW/5m7P4ZRnWNe/I3QmM74+low1l+9g\nYnwMIr1stemOzQ+e4pWqMV4VSWEYBif1fMzr6HzhyUUhk5JOMCaOURT1AoB3ADQGYAKwh6KoHQzD\n3PF0jBIr0iyBdBNZLBarSAcqG5qrxQabYS4UCq37s9n5BwJ3887OzsaKFSvQv3tXrBr/msdbnP7c\ntRcbPx/DyRwPnLuERjWrItRNiUZXVK0QhQ2zxmPqj+ux62oKZvdoU+A5H28+ik+HBLbU4pnrd1Gn\nSiwUbjpYecpP2w7hjaYv+PTdmbh2FyY7sKLVRiOmnroOUYgcQ9s1QfMq5QuMP+X3gxjZpEaBY/1h\nddIN9KhTBXweDwqxCJ91aognOWrMOnQBlpRUTEqIhZijXIyjWblY0cy7+Z98moW2vft5da2JSDsg\nOI2j6gBOMwyjBwCKoo4C6AlgvqcDlDiRtnV3+1o/2h22iWEURUEqlQZ0u5I/Qmq7P1sulweNi2zl\n8p/ww+xPUTXO8/Kb36/egP4dW3BWoGPpn4fwyzSvvU8FEAmFmDdmMHacSEKvH/7E0v4dEKHMu4Gm\nZedCqpAjPsq77U/e8tWWg1g24W3Oxjtw+iI2junj9XEP07MRyqCAFb3k7zu4rNbj8z4dkRDlOKFK\nbzTi0bNMNG1R06c5O2P/3adY1z9/8ZjoUAUW92iNi0/SMeXwBVQXCPCOn3untz16hs6VY7xOsjuo\nYjDnddeLOEeFTIhI5ycYLWkAlwHMpCgqHIAeQFcAZ7wZoMTFpG0JVDzXtkVjoPcS+7rAYBPDbFt1\n2gt0YRdKYcnKykL208deCbTZbMbZpPPo2boRJ3PYeOgUOjWrD6mYm/gtALzasiEWfzIaYzf/hU1n\nrwIAPt5yFB8HOBaddDMFNeJioPShYIgjVu8+htcb+lbze9K6XRhjk9F99nE6hh68gGo1q2Dd6N5O\nBRoAPtl4AP/j2Ir+8cx19KlXFTwnGd31osvgl/4dUbdOPMZevoMDqc99PteBjBy8Uc07ob/wLBsN\nX37V62udm5tLRNqOomhVaf9jD8Mw1wHMBbAPwG4AFwB4Va+6xFnStnApQrbxXLZimO0+6UDhy2so\nqqIktria95JvF2FYr65ejffZV4sx7o2XOfGK0DSN3w6fxoYvP/J7LHuiypTCr19+iHlrt2Loyh0I\nDQ1BRRcdt7hg7qb9+HG850lH7tjx1znfrWgAUSEy5OiNmJx4DVVio/DrmDcgE7vOIdDqjcjIUqF+\ntP8FY1homsZfD9KwrpXrMSmKQrcaFdGlWnn8dPo6Pki+g8+qVkC4Fx27dj1KQ8f4aAi8FNudWSZ8\n2X+g2+c5sqS57iVd3CkKS/rEg6c4+SDN5XMYhlkJYCUAUBQ1C8ADb85R4kQ6EK5t+4phtqveYEoS\nsy3pKZFIIJFIXM6vKEqO3rlzBzCoUba053uMM7NVUGVlolnNKu6f7AELNu7CkFfbQxCgLzWPx8Ok\nwT3RY9J8PH+uwvUHqage67q+ta8k332IhNhohPkRV7dlw8FT6Fovwad90ZPW7sLUepWw6Pwt3DGY\nMb1fZ1SOdF1xi2XC+r0Y62Us1x2LE69hQMMEj7+jQj4f/2tRCz1rVcT47SfxklKBztGe7XXenZ6D\n5Y29K5JyPUOF6q07eLSItv+ekph0QYqiLGiruCi0sqldv+BkcoHnUBQVwTDMM4qiYgH0ANC0wJNc\nQNzdLrBYLFCr1dDr9VAoFNaMaC7P4Q5PxzebzVCpVDAajVAqlZBKpUG1gLBYLFCpVFj+w/d4+43X\nvDp2ypxFmDLQu2OcYTSace7mPbzasiEn4znjxv1HqBwfj5ULZ2HurkQs2nooIOeZsWEPPuj9Emfj\nbT50CoN82Et8/3kW0jOy8MnpG2jYoAZ+GdXLY4HO1uig1ehQy8PnewJN0zj3JB2vJHhf3S0qVIE1\n/TviqVKGz6+muO2mt+/Jc7SrFAWhFz3QAWDLcx36ve15Nj7J7nYNxecX+Y8TNlEUdQXANgCjGYZR\nefO6SqRI+7tXmm0lqVKpIBAIoFQqnSZcFVbZTlePabVa5ObmQiwWIyQkxOv92YGYP3tdbK/lvXv3\nEFMqBCFyz4uQ3Lp3H2UUYsRHe7fv1BkTf/wV4we8HvAFzGcrNmPc8EFQhijw3YzJkETHoe+8VdDq\nDZyd4+87D5AQG41wJTc3601HT+Ol2lW8TszLVGvR/5tf0bxOAta/1wfd6lVzf5ANE37diw+acZss\ntvDEZQxpXMPn95nP4+HjtvXwVtt6GJN8Bym5zrcq7niWjf7VvVsMpGSrUaFRc4g9zIkgHbDcU9R7\npJ3tk2YY5kWGYWoxDFOPYZjD3r6uEinSLL4IKGuRmkwmjy3SQFvSzmDnarFYEBoa6ta97c3YXMCW\nHGWv5brVKzGwu3dlMb9c9AM+6d+Nk/lkqtRQ641oVIMbt7kzzl65iYRqVREeltcliqIoDOr5KqZ8\nNBb9Fv6Kwxevc3KemRv24MM+3CWlbdx3Am+1ru/VMbO2HcPA5dvRuGosPu/RxuvWns9UasBkQjUH\n7Rx9haZpJD/LRqeq/ld3axYbgZX9O2Jleg7W3X9a4PFDT9LROq4cRF4ubNY/yUWvwW9Bo9FAr9fD\nZDJ5tSVSo9FALucmxFFSoAT8Iv8JBCVSpH2xpBmGgUajQW5uLiQSiccWaaCFztFrsJ+rQqHgrJUi\nFzAMA7PZDL1eb7Xuz549i9qVYiDyYgvY0cSzaFg1FqVDuUmQGbd4LSYP7cXJWK6Yu34nxgwt2J2r\ncsXyWLVoFnbdfIrxK/7w6xxJN1NQo1J5zmLRGw8lokudahB6eKM5eSMFPRZvQs2GDRAqFeGTbq18\nOu/4tXswvqX7hhLeMOfYJbzdrBZn380wqRg/9m6DsNhIjE++A73ZbH1s67MsDPTSin6k0iKyXmOU\nLVsWEokEfD4fFosFer0eGo0GOp0OBoMBZrPZ+t13VMyEJI7lp6gzuwMVEw+eO3sA8FSkjUYjcnJy\nwDAMQkNDvSqTWdjJV/7M1RFcz5+17hmGgVgshkSSV1xj49rV6PFSW6/GWvbLb3i/Fzfx1psPn6Bs\neCgqceQ2d8b+0xfRuH5dhDixckRCIb74cDTadOyE12Yux+PnmT6dZ+6m/RjXmzsretOBkxja2nUt\nbwBQafUYsuxP7H6QjTWzPkZ8VAQqhcqt+8K94U5aBkoJ+YgN405sjGYzbmep0Tae20Q9iqLwduME\nTO3aHB9du4/z6dk4lpqOFrEREHtpQa1/kou33vsAFEWBz+dDKBRCIpFALpdDJpNZQ2tGo9Faapim\naZjNZmu9fX+zu2fPno1atWqhdu3a6N+/PwwG7sIwRUVRx6NdxKT9osRld9viToAsFgu0Wq21yYQv\nhT4KK3EsWIuSsNh3/rJYLFbrfu/u3Wjb8AWvrP1fNm/H660agAcezl69jaQbd3AzNQOPM3JA8QUQ\nicUQiyUwGA3QqdWoU7EcBr7UApWiHIvwpys24fuJ73LyWl3xw7bDWL7AcScjW9q3bII6Napi/OyF\n6FyrIoZ2bO7xORKv3UHtyrGcNRhZf+AkutZPcBuLXrj7FE4/Tsfno4agamxeI4svf/gFPwzwrY76\nlI0HMK+Dd+51d3xx+CLGtHyB0zFtqR4RhnUDO+HTvWdx6vZDbHujnVfHp+ZqEVazrlOB5fF44PF4\n1oxv9ruv1+vBMAz+/PNPjB8/HvHx8dZwUtOmTREa6nm4ICUlBcuWLcO1a9cgFovRt29fbNiwAUOG\nDPHqtQQbpAtWMYRtxWiP/VYlhULhlzUaaEuapmnk5OQEpDY4F4sMs9kMjUYDHo9n7fyl1WrBMAws\nFgv27vwTM8Z6Vg3LaDRizg9r8NfZJNSsVhXnH+9BxdjyiK/dGE27RCEmqhwkdsk2JpMZf1+5ipV/\nJb5gahsAACAASURBVOLh4wPQ5OaiWlQ4+rVvjhfiK+DI+Suol1CZM7e5M347eAIdXmxRYH7OKBNe\nCsvmTcPKjX+g5+yVmNi9DZrVqOz2uAVbDmLFx9zV6N586JTLfdFJdx9hxs5T6PNye/wyepj185d0\n9SZqRoahlA9FVJLuPkblMDnKKrgpwAIAaoMRmTojGldw3HKUKyRCAbpUi8EzvQGjjvyNuc1qIMLD\n1/HrYxU++OxDj8/FWtsURUEkEqFv375o06YNPvroI9A0jZkzZyIpKQkzZ87E++97Vj2PTYTVarXW\n72pMTGC7sxUGgbJki5oSKdKuYtKsoHDVPzmQMWm2sxaAIitK4go2c9tgMBQo8MJe+7VrVqN3p9Zu\nr1Pqs3RMX7wSBkYAtVqNKR+ORYvGDTyah1AoQKN6ddCoXt7WIYvFgqs3bmHriUR8veMvJF+5hnlj\nBvj3Yj1gw6EzWL1ollfHUBSFt9/sib6vdcHiVeuxYNtxzB74MqrEOPYInLh8Cw0S4hEi40bc1uw5\njm71qzu0ou8/z8KnfxxFZHQUVs2cCIXdOb9avh7Lh/jWH3vW1iNY0rWZT8c6Y+rB8xj3YuBbUQLA\nigt38Mu7PZCt1eOjX/ehXdkQvJHguoJemloHebXaXlm9LLYx6XLlysFsNmPmzJkIDw+HyWSCXq/3\neKzw8HB89NFHiI2NhVQqRefOndGxY0f3BwY5gUrcKmpKpn/AAbZblbxJDHNHINzdrOs4JyfHKsyB\nEmhf52+fWe4oNq7RaHD14jnUq5ngdJykS1cwaMIMzFmzDcPGTMLEqTMQKhN5LNCO4PP5qF2zOsYO\nH4qG9eqgf7++2H/9Kd78YjEepvle9tEVP/6xDz1e6eTz+6SQyTBp9Nv4aton+O5IMgZ9/QueZRfc\nTrnwz8N4rwd3N9Rtx85gUKv8sehDybfwxveb8V3iDUz7YDhmj32rgEAfS7qEhrERUPrQ0ONA8i00\niioDpRcVvdyRodGDpnioyeFea2fsuXYfL9aoBIlIiHJhIVg7qie0YaXw3pG/YbRJKrPn10c5GPaB\n51a0La5qdwuFQq/i03fu3MGiRYuQkpKCJ0+eQK1WY926dT7NK5hg+zUU5U8gCC7TjGNYAWIrhgkE\nggIVw7g6B1fYl/Tk8/nWeFQwFCdxZT3bs3LZj3irx8sOH1u/fQ/+PHwateo0xKezFkGpzLMuJo0b\nhSnvDedkrmazGfuPncTyxQvB4/Hw7Hk6Zi5eCkabi4VjB0Im4aZjFE3T2H/+GlYvGuT3WGXCS2HW\nx2Nx/1EqJv+0CkKTHgve7g6ZRIzDF6+hcY3KnPWL/nnXUbzesAb4PB5omsaSA2dw5E4qWjSojWUz\nxhcQZlu+X7sZa4a96tN5l+w7jRWvt/R12g6ZciAJUzoGtkANy5pLd7F2ZE/r7xRFYWynxrhcoyJG\nbDqI/yVUQOOY/JXK0rV6iKvURHg4N4sIi8Xi84Lw3LlzaNGiBUqXzitX27NnT5w8eRIDBgTe2xRI\nSqolXSJF2ramttls9isxzBO4EGn7xCt/s7Y9xZtFhm3s2d1i5/nz59DnZKBCdP4eyqs378CeUxfR\n4aWumP/t8nzvyfWrl1E+IgxxFcr79mLsmLFwMd4dNtg6z4iyZTB72qe4duMmhi34CTWiwvHp0J5+\nL9pmrt6CoX16cLr4q1g+Ct9M/wRXbtzGOz/9goohEtx89BRrpnCX/Lbzr3NY8U53vL92N54baPR+\nqTV+HTHU7evY+9dZtKpc3m09bkdsPJWMDvHRkAi5u/U8ylZDKZMgLjzwxT12Xr2HdrXiIXYw/xfK\nR2D96N747I+j2PPoGj5t+m+Z03UPsjHy+699Oqez76ev94fq1atjxowZ1pycAwcOoEmTJj6NFVRQ\nwekYpijqEwADkddYIxnAWwzDeJxOXyJFmhU8nU4HAJwnW9nCxbiOEq/sz1GUlrQ31jPLT0sWY/Qb\n/xYheZSahvHzlqJVu874evEKh8f/8O08LJn9KSdzzszKQUaWCk0bFbSuaiRUw9JFX+Hw8RPo9dli\nvNG6Pvp3bu3TefR6I64+fIbxH3hVjtdjaiVUwbJ507Bw+S9QP3yGYd+sR4iIh/a1q+D1Vg188gZY\nLBbMWLMVaTm5+Hh7It59syfqVKvk/sB/+HnTDqwd7luZ1o0n/sbqnvmvNU3TSM3V4sazLNx6no3H\nOhNKiQXoX7cKIkPcZ7B/fugC5nAc33bGuuQUrBvV0+njEpEQ8/p2xO7kOxi6PxGzmlaHRCAAL66a\n1XL1FVvjwx/DoG7duhg8eDAaNWoEHo+HBg0aYMSIEX7NLRgIxsQxiqLiAAwHUINhGANFURsBvAlg\ntadjlEiRNhgMMBqNkMvl0Gq1ARU3f9zdvogf17ibv9lshlqtBp/P9zhUcPXqVUSESBCqDAHDMPhy\n8c+4n6HGpzO/RunSjhsW7Nq+Be1aNEYIR/WIJ8/+ChM/GOvyOe1at8SLLZph/aY/0GPqN/ik38to\nUsu7kpYTl67D+2+772LkL+eSr2P10m8gEYuR9uw5zlz4G5M2HkF2Vjb0GjWqR5dGr9YNULdKRQB5\nvZnPXL2D09fu4WZqOrJ1BkikMoglEkilUlxJvoWNCz5HpBeNTgBgy4G/0LFGnENL0hVGsxkDv/8d\n6WotRuw+A6FAALFIBJGQD5FAgDIhclQoUwp142LRJSwE6blaLLt4E4/Tc2DQ6dE8KhR961QpEMe+\nnpaJCuFKlFMGvvrW1uQ76Fi7KkQeuJlfrl0ZjSqWw/j1+6DRGPDdlnk+n9fZAt2fe8XEiRMxceJE\nn48PSoqgwYYHqACYAMgoirIAkAF47M0AJVKk2So+/q44vcFbS9dkMkGj0XgUJy/sgilA/gWEXC6H\nSOS5a3PFj0swdUR/JCVfw+xl69FnwFsY3raD0+fTNI192zdj1bdzuZg6Ll+/gXLlyiG2gvttJXw+\nHwP79kav17pi9oJvsDPxEqa93duj86Rnq6C1AHVdJMZxwdZ9h9G21b9buyIjyqJb547o1jkvgcxk\nMuHazdvYcyYJi/cngaIoyGQyVImvhDptOqJ7xViULVPa+vlctnodXqwR57VAA8DG7fuwYWR3j59/\n/t4TLDyYBJFMBo2ZxsEv/+eRyAFA6xrxAACN3oDj11Mw/+9beJaVC9pkRPsKpdHrhXjM/usyFnf3\nrdqZt2y8+gDrR3lesa6sUo6FAzpj5ukHiIjgbltYsOSnsGRmZiInJwd8Ph9yuRyhoaFF0x43CC1p\nhmEyKYpagLz2lDoAexmGOeDNGCVSpG0z7QItbrbn8eSLw/alNplMVuvZEwL1OhwtALxZQNhz5PAh\n1K8aiw9nfgtJqQjM++YnyGSuXZaLF83FOwPf4CTbHgDmLV6Gb+Z7txVKKpVi+tRJ2LXvAHpOXYTl\nE99GuNJ1xuz479di0tjR/kzVI37bsR8rvp3v9HGhUIg6tWqgTi33rR5pmkZiYiI+mO29FfXDbzvQ\np3ENt0VPzGYzvt53GkmPM1GvehV8PX4EvtmwHYOb1fRYoG2RS8ToUi8BXerlLYay1FocunIXb+04\njacqNe5nqhAm4yYJ0BmbLt3yqmwqy4ozNzH+c+fvnSfY31sMBoPHjTkCRUZGBo4ePYrHjx8jJycH\n6enpMBqNCA0NRZ06ddCyZUuUL1++cMsVB2ExE4qiKgP4AEAcgBwAv1MUNYBhGI/T6UukSNsT6JWn\np2OzZf5EIhGUSqXHH+DCWjWz29TYUIE31jOQJwDTp30OiUyJUWPHo2Yt93tW1bkqPH1wB23eG+rj\nrPOzdfd+tG7Z3Ge3+SsvdUS92i/gnRmzMLRTU7zWqrHD5928/xjhZSJQsXxg+kSzrNm8Da927siZ\nZfLtjyvw1msdvf5M0TSNIyfO4LfRzuOxlx+mYf6+sxBKZej7Uit81KAWeDze/9k767io0u+Pv4du\nMFDsRsUO7M7VtTvW7m5FwaAUQRTE7m7d0NXVVdfutXVduzuoIYaZe39/8B0WkJg73EGW375fL167\nMveJO8zc85zznOdzUEbH8Ozlaxp10G/fPzk5bKzoXLM8285e56dZIwg5cJrgS38zv0U1HGVSYUvO\nvr9esn2kNN33T5FRqHLkz7AXnVIt6W+t233s2DFOnz6NqakppUqVokqVKhgZGfHu3TtOnjxJYGAg\njRs3xs3NLcN78bryLTzpU3894dRfT9K6pDpwThTFTwAKhWIfUAf4/22kEwtqZEbSVXrhaK0oiUaj\nwcbGRnKWuSHD3dq+M+I9a1m+YiW16jen/6DhOnvFcz2nM2WkPOpZgiCw58BvrFmyKEP95M/nxKqQ\nRQQtXcmRRetZPK7fV+/HzLV7WOg5PUPjpIcgCBw+dYF1IYGy9KdWq7l7+zbuPSdLbjtv9Q6GNaqa\n4vdozYmrHLn/kgqliuE3fhBOuRySvD4peD3T2zfSd9opsuf8DZpWLkNeBzt8fvie5x8+47XzMFaC\nGt9m1TExkc+r2nX9Ia11kE1NzpoLfzPIU56/XfLiGt+6AlbJkiVp3759ih59//79Adi0aRORkZGZ\nZqS/RXZ3A5cSNHD5RyVw7k9fVaK8B8xUKBSWQAzQDLgkZYxsaaQzm9SMaOIz2ubm5hmWHzUE2jlq\nj6lJ9Z61KJVKHjx8zJgJbjq3uXvnFvlz2VGyWBG9xkxOwLLV9O3VXRav09jYmEljR3Lu4mU6uAcR\nMvYHiuSL94hOX79DeZeyCaUoDcXyTTvp1rGdbCHD+UFLGdG1teTPoEql4u/795nVuGOS3196+IJ5\nR67QuWk9tvftnuI8X73/hIk6jnKF5C1ssu3cTXZNHZDw78KOOVk1uicX7j9jwL6j1Mufg2G15Kmu\n9dPfL9gxSrc8BS0fI5QIjoVwdHTM8PgpVcCykSnBUl+qVo0XG1qzZg158uShTp065M4dnxSqzQXq\n27dvps4pi+5J31AoFJuAK8QfwboKrJLSR9YL4stMZiVdJR9Do9EQERFBTEwMtra2WFlZ6W2gDXUP\ncXFxxMXFJVTU0tdAAyxZspQuPaSJeaxaPJ9JI3TT9E6P0PBwHj97SZMG8iYR1anpSlCAHzM27Gfd\ngfhVctCe3xnV7+tSlHIiCAIXbtyhVdNGsvSnUql4+fwp9atIN1zTg9Yyofk/R8xCldH0XbufXx5/\nZLPneHq3rJfqQmJayEbcO0krQpEeiw+eoVdD1xQ921rORdg5bSCOxYrRY+cJTjx8kaGx1l66S5ea\n5TGWuFBae+kBg8bqpy6WHlkh3K3RaAC4f/8+GzZsYOnSpfzxxx98/PgRhULxbUrnGim+/U8KiKLo\nL4piOVEUK4ii2E8UxTgpt5UtPenExjAzjHTi8RKLklhYWGBhYZFh71nue9DuPcfFxWFiYoKJiUmG\nvlTPnz8nMlpFvny6i/Tv2bmZ1k0bYCNT2M7NJ4BJBkriypHDgZBAP9Zs3ErLCb60bdkUSwvDJu7M\nX76e/r26yxZ58QpYxLie0s82h0dGEf7pI9WL10EQBHwOnOVhaBSzhv9AiQJOaba9fv8xxXLbUSCn\nfBEHjUbD6b+fsat9k1SvUSgU9KxfhY41yxO0/yRrdp3Et2lliuSSNg9BEDj25B07W0vbS/8QrkR0\nLCRbmDctSdBvhfb0jL+/P6GhoWzfvh13d3ccHR3p378/DRs2lE1dTWeMsp4nLQfZ1pNOq8iGIcbS\nqpuFh4cTFxeHnZ0dlpaWWS68HRcXl1CP2s7ODhMTkwy/PyEhS+nWU/cydyqVivMnjtCjg36yksm5\ncfsuTk55KV5UnrB5SigUCgb17YXG1JpfT13mxt2/DTaWSqXi7yfPaVBbHhWoSGUUEZ8+Ut2llOS2\nUxesZFrrOvx28z5dVv5CdddqbJw1Nl0DDTB33W6mtW2gz5RTxWPnEca2baTT98rCzBS3zs1YNqYn\n8y8/ZNn5O5LGCj5zi34NqkpewK69/ICBYyZIaiOFrBDuhn+esbGxsTRs2JBZs2bx/PlzRo0aRatW\nrThw4EDmHh01Mvr2PwYgW3rSicmscHdsbCxqtdogkp5y3ENi71nK0a/0uHDhAoWKlUz3mFVi5vt4\nMH7YANneowXL1xGyYJ4sfaVF0PI19BkwjOo1ahM4bw5FTl9k6jD59908g1YyrL98AimefguY9EPH\n9C9Mxuv3H4kOD2X2L2epUq40230mYaajiMnBs39St1Rh7GQ8GqWMieXVl0jquxSX1M7R3pY1Y3qy\n9tgl+u85xbJ2tbBK5/MvCAJX34UypXP6pUMT8z48EkWewrImS6XkSX/rcLeWkJAQXr58yfXr13Fy\ncmLp0qXUqVOHJ0+e0LBhQx49emQwOeavyIJ70nKQbT1pLYY20tp9XUEQsLe3lyW8LTcqlYqwsDCA\nr/aeM/L+CILAps3baPW97uIWL148w1SIpbIOZ3p1YfPuH2nZvAk2NobNdo2KiuLug6c0aNQUKysr\nZnr741iiIr3GzyI0PEK2cSKjovjwJTyh7GZG+RIahhAbhUuJtMsoJkcQBHq7zcPczp6Fk4Yw9Yf2\nOhtogPU/H2FUS3mlUidtPohbF/0qgCkUCgY3q8mcfu0Z8NN5zj15k+b1vn9cY1gTV8nf5bWXDOtF\nQ9bYk4b4z8iVK1eoUaMGhw8fZuPGjdSpUwdRFClWrBiTJk3KPAMN8dnd3/rHAGRbTzrx0StDGOnE\nZ4pNTEwwNTU1WLKEvvcgCAJRUVGo1WqDFBjZvn07TVu2lnTfC+fNZuFseeQI1Wo1R0+dY83SIFn6\nS4tZcxcwbHTSRKBWbTpSuYorw2a5M6hjS1o0rJ3hcdzmLWbcsIEZ7kfLLN/5ePSTdr5377GzBO06\nSJ1ypQkYIz1SsHzvIbrUqqCXcElqvPkchsLYCJdC6YfZ06J0gTzsnDaAGZt/5ejjN8xq+nVJVJVa\nzcNQJV5lpW2fvAuLxDhfMdn3YkVRTPIdywpHsACMjIzYuPEfCWpBEDAyMkpY2IwbNy5zJ/SfJ/3v\nxBBGWuuZarOiDS2Bp889qFQqwsPDUSgU2Nvbp2qg9X1/lEoll65co3KVlMU+UuL3w79Su0oFcuf8\nWo7y0+dQjp8+y4oNW7l9T7f9Xvd5gYwePsTgkYsXr14hmlhSyrnMV6/lK1CQwCVrOfXXCyb6BiEI\ngt7jvH7/HmMzU5xLSgvnpsaLV69xsDSlRCHdBFeevXlHN/dAHimNcMphj8cAaceOIH7hdPLSdXrU\nriC5bVpM3nII9y7NZenL3NSUwIEdcK1agZ47T/AxMirJ67N+/5PxLaUX7Fh98T4DR4+XZY6JSSnc\nbWdn+IpfuqBWqxOeH98kozsxRsbf/scAZFtPWoucRjo1z/RbaGunhqG9Zy3xR65097Kio6NZEexP\nvTq1GDJ5FnGCiJmZBabm5piZmWNr70CRosUpUL4uhy7eYNm2X4gMD6VwPke6tmlJpWTh8Rev3hCn\nEalSsbzct/YVnv7BuM1OXVfcxMSE0eOncfniObqNnUngtJEU0UE3PDkeAUuZ4yZdaCQ1vOcHsmh8\n/3SvEwSBKYs3EiGY4O07l5s3b2IWVgJ7PdS7pi3dzMQ29WVdOF17/JKi+RwpmFu61nhadKhZnuol\nCzJ+9V56lC5Im3JFiVKp+KRSU6O4tL/fy09hWBQqha2tbYJHaSiUSmWW8KSBb6LRnSrfepFgILLQ\nOywvyY9FZYTkoiQplb40pJFWKBQ6eWiJZUd1Lc+pzwLj2bNnREaryJ8//QfZixfPWLxoIX/duUmv\nfoOp7lobp3wFsE4jO7Vm7fizzqIo8ujh3/x+6jgrdx1AGRZKwby56dKmBYvXbGLuHA9J89aHC5eu\nULJ0eXLnTl+UwrVmHZxLl2W2lzv1KpVicHfd9+rv3n9EgQIFyJdXnkIMN+/eo1SBPOkW0dh77Cxb\nj11k2NChVK8WH/rduWUTO2aPkTzm+y9hRISGUquUtP3v9PD96QTrx/WWtU8tBXM5sGPKAHz3/M7R\nAxcQNBomfVdHcj9rLj9k5Lxg4uLi0Gg0KBQKjI2NMTY2xsjIKEkYWCopiZlkhT3p5Gi1IWxtbWXT\n4ZdENj2ClW2NtJaMrug1Gg1RUVEIgoCtrW2KK8dvnSiW2HvWR3ZUKsEhSxg4NO39ppMnjrFzxw6c\nCjnTqvt4zH5aQvde/SWNo1AoKFmqDCVLxYeZRVHkyaMHLF66iBfvP/PTr4cZ0q+XvrehE8s3bGN+\n0Eqdr7d3yMG8wKX8tHcH3cfNYnj3NjSuk/5RqnnL17PId04GZpqU4KXLWe0+KtXXn715x5QlW3Gt\nXYcVy5YmPFQ3b9lK10Y1JCWJaZkSvB7fLqmfX9aHPRdu0rhiaWwtDVdAw9jYiFndW3Lg8h1mbdmP\nlZm0h/2j91/IXbZyQka3VnFLo9Gg0WhQqVSIophgsLXGW9/nRmRkZJYJdydeQLx9+5Zly5ZRuXJl\n2rVrl/lFQLJYwi6AQqEoDexI9KviwExRFBfr2sf/CyOtj5criiKxsbFER0enK0pi6HB3Wv3r4z0n\nR8rcjx8/jnOZClhaWn71miAIrFu9gj+vXaeiaxMm+WzBwtKKuZM7M8sr40ekFAoFRYuXRKmMZM3W\ngxw/8gu9h09kUM+ONGkoT/GGxGzbvY9GzVpjYfH1vaY3z45detK6bUe2bFjD6t2zmTGiD+WdS6Z4\n/ckLV6hUoRz26VTd0pU/Tp+jpksp7Ky/DleHR0bhsWIrMcYW+PjOJVeuf5KcBEHgwolj7PSSnvBz\n/f5jCjnYUFjGkLQgCGw7e5NdU/vL1mda7Llwk1Xuo5m37zAVHW0Z27S6Tu3WX32CW/A/So/amgFG\nRkYJC+bkRlsbEk9utFP6/mZFMRMtCoUCjUaDsbExJiYmFClShN9//51bt27h5eVl8NB/YsQsmDgm\niuLfQBUAhUJhRHwt6R+l9JFtjXRGxEw0Gg1KpRIAOzu7dEM338JIy+U9S62BvXffz0yYOjPJ70ND\nv7AwwI+wyBiafP8D7r09Evo9c3Qvrq6u5HaUJ4y7cL4XvQeMwtTUlJbfd6ZJ87Zs37ScjbsmM3Pi\nKEqWKCbLOIIgcPiPcyxatk7vPszNLRg0bDTh4WGsXRHC+7Xb8Z04jPzJQtort+1j5SK/jE45gY1b\nt7HFK2km+u0HT5i/9RcsbHPQp89Ayrl8fQRuwYIFjOrcQq+F3tx1u1g3NPUKWfrg/8tJBjavLbmw\nhT48efcRO3t7qpYuzmq34Wz87RS91uxn1Q8tsElDXe7Oqw8UqVIzxUVrYhQKRYK6H8QbXkEQ0Gg0\nqNVqVCoVQBKjnVqIPCoqKkvsST9//hylUknZsvGfpbx58zJ06FAGDhyYcJ+Zmkz2DQpsSKQZ8EgU\nRUlatdnWSGuRYkATS3pKFSXJzMQxrfec2v64VHSd+6rVq2nXKalU5crlIfx17zHdh8ygcLGk2c9q\ntZqTBzexaOnaDM1Py/t3bwkNDaV6zX/0uU3NzOg7eBxhoV9YvSwA5Zd3+M6cgn0Gw4E+AUH0GThM\nloeMnZ09E6Z68O7tG3yXLYKYCOa7jcbGyopd+w/TrFF9LGQKDe7++QCt61TDwjz+LPz2306y5+QV\nyri44DHHi9ypiGxERip59/QRDft8J3nMPcfP0aRcCVmFS2JUKm48f8u0ri1l6zMtZmw9xMIJ8Try\nCoWC/q0a0qBSGfqHbGJQzTK0qpSyWtuWm8+ZtXSO5PES71nD1yFytVqd4IVqfy8IQoJCYEb2fEND\nQxk8eDB37txBoVCwbt06atXSPZtdO6/79++zatUq3N3dqVSpEs+fPycoKAhLS0t8fX0TPOzMQsz6\ne9I9gG1SG/1npP+HWq1GqVRiZGSkk/ecfAxDor2HxCUvU9sf16dvXXj//j3PX7zhu7bdAbh39zYL\nFwbSrG1/pvSdk2Kb1QsmMHjYaNkyQP28PZgyM+Usa3uHHEycMZcXTx8x1duf/LltmTllvF5G9vPn\nL7z7Ekn1Ghk/95yYvE75mOnlz6MH9xntE0SBnNY8evacDUsWyjbGwUO/sWH2eNyXbeHB2880adqU\nJUtC0lWY8/H2Ynqf9pLHEwSBHYdOsGt8zzSv+xgeSU4bK53/HpO3HGJa5+aZku/x58PnlCxaiLw5\nk5bYLJ4/Lzu8J+K7aR+/7TjKom5Nksz/2vN3lK3TWBb1vtRC5Gq1mtjYWOLi4pg+fTqnT5/G2tqa\ndevWUa9ePZydnSW/R+PGjaN169bs2bMn4bknBe17ULduXf766y88PT2pVKkS165do2jRokyZMiXJ\ndZlGFvakFQqFGdAWmCa1bbY10rqGu0VRJDo6mtjY2AS5TKkfekOHu7Ur6bCwsG9W8nLhoiB69hmC\nWq3Ga44HmNoxZe5WrKxT3kd99eIRxmIMlarqfo46LY4dOUj5StXI7Zh2ycNCRUvgFbCSa5fP0W/0\nNLq3a0Gb76Sdr53h48+4KbMzMt00KVHKGb+Fy/Ca5YbGxIbBU70wN4J61SvS7vuW2Om53+gXtIQP\noeGMDtlKz549mFilik7tXr1+g5WoomzRgpLHnBi0HjszIzx2/c778GgiYlWYmppiamqKmZkppiYm\nmJmaYGttxcfQcL6EhpHb0owf6laglnPRFPt88zkMtQiVi0k/xqYPfj+dYPWMlIuzmJgYM3tgV87e\nvEfnlT8yv0M9nPPFZ/pvv/0S7xU+BpuXNkSufTYtWLCA27dvM378eI4fP463tzeRkZGcOHGC8uV1\nO4oYFhbG6dOnE0RItPXj9cHS0pJatWpx+vRpPD09mTx5Mv7+/knmn6l8gz3pU1dvc/qaTprwrYA/\nRVH8IHUMRTrGJWsc/tUDQRAS5DrDwsLIkePrhJa4uDiUSiUmJiZYWem+yk+O9uiBg4ND+hdLRBAE\nIiMjUavVCQUx5ESXuV+8eInzl65hYWnF7j376DnEHedyaSfVzJ3UCc+5AeTImXENY0EQGDeiqKWb\naQAAIABJREFUP/4hmyTdv0ajYf2KQELfPWP+nOk6/X3/vHaDg6euMGaC5AWvJFQqFVMmjGL+4g0o\nFApCv3zm5rWLXL10ltDPH4mJiqBU0QK0/64ZFV3itxGioqK5evMW127d5dHz13wOC8fUzAIzC0uM\nTcx4/ugvQhYF4uQkrXbz6JEjCR7ZA6dcun1+I5TRzN3yE/defUAVGcHUfl1wzGlPnpz25LC1SfN9\nFkWRJ6/ecvDcVW4/eEpYRATOjvYMbFiV4k7x9Yh7h+zAv397Cug4n4xw+Opdbn9UMqH79+leGxYZ\nxZQlmyiX0wrX4gV4WagqnXsY9nSBIAhER0cn7EGLokjr1q05c+YMAK9evSJ37tw6Z1Jfv36dYcOG\n4eLiwo0bN6hWrRrBwcGStPfVajUmJibs2bOHZcuW0b17d+rWrYunpyc5cuTAz88vueqawa21QqEQ\nI8/uNfQw6WJTtzOiKH51vwqFYgdwSBTFjSk0S5Nsb6RFUeTLly9JPjSJk67kKDah0WgIDw9PcSGg\nL4nPZpuZmaFSqWTtX0t6RloQBPoPGMSnL5GULFeLDr3HYZyOoTy6fwummo90791fljkumDeb+o1b\nU7VGXb3aX7tyno0rF+I3awpFCqXtLfYdMYH5QSuxtJQu5CEF79lutOnUB5cKKXu7arWaB3/f4cqF\nUzx/8gCFwggrG1uKFCtJkWKlKFi4GLkd8yYYxEVzp9OhVeOEs866cvHSJW78cQj3vukX4Pj90nXW\nHjqDQ67c9OrcnnVbtjOt5/eU0cMD1yIIAjfuP+HXs3/y9NVb3n/8hJ25CdunDNC7Tyl0DtjIljnj\nMTfTPfFy82+n2f3HBfb+dtTgId3kRloQBNq2bcupU6f06u/KlSvUrl2bc+fO4erqyvjx47Gzs8PL\ny0tyX7t27aJYsWK4uv4TLRs6dCiNGjWiV69eiTO7M8VIR5z/2dDDpItt7fZfGWmFQmENPAOKiaIo\nWeg/24a7k6M9xiDHkaXkyB3W0e49a89mKxQK4uIk1QnXmfRC9XM8vXn7KYqhkxaQJ1/6WsYqlYpL\nJ/YQlIGs6MS8ef2K8PAIvQ00QJXqtSlRajW+3lOpX708fXqkLHe5Ydsumn/XzuAG+tPHj8TEqlI1\n0BAfhixbrhJly1VKt7/w8FAiQ99LNtAA61etYItH6nW4QyMi8d38My8+R1KrRjUW+XljY23NX/cf\n4mhjkSEDDfH7llXKlKBKmfhqU13c/Klc0YWuC7fg2705zgWkRQWksOHYRdo0qCHJQAM45XZg2PhJ\nmbLnmtLxq/QyydOiYMGCFCxYMMGwdunSBT8/aScLLl26RNGiRenWrdtXr61aFX8ULS4uLnOLa0CW\nPCcNIIqiEsitb/tsa6QT70nDP96zRqORXfBDrj3p5Mpm2r1nQRC+iezop0+fePs5FveAHTovRJbP\nG8mocVNke4D5+85k2uwFGe7Hzt4Br4CV7NyympGTPQiaOytJBEWlUnHi3GUWLZVncZEW87xnMnry\nHNn6C/SZyqTRIyS327Z9O53qV8fS/OtI0qHzV9lw5By5HfPQu0tXKrgkzdyfHxTCmunSx0yLjfuP\n0aZRbfq2bc7nsJb4rd1O2KeTLO7fDhsZM8ch/nmw/9rf7PSemP7FydodufmYeYOnyDofXcnoGWkn\nJycKFSrE/fv3cXZ25ujRo5QrV05SHw8fPmT//v0ULlwYZ2dnChYsmLBwiIuLQ6FQsGXLFjp06ICL\ni4vec5XKvyC7Wy+yrZHWojVu4eHhBk+6Sr7qlUJaymaGTExLq2+/gGDa9Z6k8z39desSjrnsKF1W\n2pc+NQ4d+JGqrnXJlVueM9YKhYIefYZy37U2/UZNwX38cMr/TxN89twFDB4xzuDJLvfu3iZv/oLk\nK1BIlv6ePX1ELntrihUtKqmdWq3mzLEj7PJKWhDi3rNXuK/dS53aNQme74u11dde255fDtGsegUc\nbOU7q6tWq/n1/FW2zXcHIKe9Lf4Th3L/6UuGr9lKiRw2zO7WXLbF34Kf/6Df900k97fn1BU69uqb\naUlRKUmCZvSMdEhICL1790alUlGiRAnWr18vqX3Pnj1Zt24d165d4+rVq1hYWGBsbExsbCyPHj0i\nLCyMgQMHUqyYPJoFOpOFs7szQrY20olFSaytrWU5KpES2i+RPkY6sfecnrKZIUk+9wsXLmGduyR2\nDronfu1Z601A8ApZ5qNSqTi0/yf8l2ySpb/EOJepwLzgDSzy86BE/vN0bt+KGMGY8hUqyz5WcpaG\nBDLbb7ls/S1fMIv5PnMkt5vn58eEbt8n/M2jYmIYu3gzNjkdCZrnhYN9yufMBUHgwMGD7PSdlIFZ\nf43b0s2M79PlK6PpXLQg632m8fuFq3RetI2eNV3oVk96WD8xKpWaq0/fMWlAD2nt4tT8+fwjnSdI\n1/aWCzl0uytVqsTly5f1bn/8+HEGDRrE58+fefnyJU+fPiUiIoKcOXPGCxfl1juymyH+86T/ZYii\nSHh4OBYWFpkiTaePYdUuIkRRTPPcc0YWAemRUn8ajYbVG7bTZ2ygzv1sWeFJt559sLKSx7vynePG\nkDFTDSaGYGllzQyvRRz8eSc/DJ9A8NI1BhknMUePHKKqaz1sbeXRXb504TQVy5clZwqlP9Pi8+fP\nRH14Q50K7QBYsH0/Vx69ZtKooZQpVSLNtt4BwYzt3kbWv8u7T18Ij4qhVsWvVdC0NK9VlSaulVi7\n7zc6B25hVsdGVCqu33741M0HmNSrneTv0qbfz/LD4GF6jakvKXnS31oSdNKkSZw5cwZvb2/8/Pyo\nWLFiktcN8ZzSBdHw+WnfhGxrpI2MjBKyobVZ3oZEqrKZrrrgmY0oioQsW0mD1gN0Xth8ev+GL+8e\n0bCJPEXe7965ibWNHWVc0k+ayig2tg6Ur9oIX29v+vXrS516DQ021o97dzF/8QbZ+tu9cQnLFksX\nQvGaM4e5Azpx/MotFv98nO4d2zN09Nh0P4MfPn3my4e3NKgivc50WkwKXs+88UPSvc7Y2JihXb+n\nR6tG+K/fxdIjF1g2uIOkY3kfwyNRakSqlZFWs1sZHcOzCDUDyhm+NGpisqKRrlixIr6+vmzZsgVH\nR0cKFSqEpaUl9vb2WFlZUatWrW9SBUs0yp7mLHve1f/QGs7MqPes6xiJvWcpymaJ70VuEiuaPX78\nmAdPP9K9ecX0G/6Plf6jZSmgoWVZcAC+gatl6y81BEFg1/ZNeATGn6/cvHQmJ08cZ7qHp+xjrVu9\njDYde8iWsPjz7i20at5Uspzo7Tt3sDeFaSt3UtalHGuCAzDXcRvIw9uPecOlhYjT4+yNuzgXLUKB\nvOmXAtViZ2ONz5gB/HnnPp0CN+PfqwVlCuXTqe3E9b/gOVx62cs1h04zcIQ8i9CMoFQqv3mZSnd3\nd7Zs2YKlpSVXr17l3LlzKJVKYmJiCA0N5erVqxnKQNcX4b9w97+XzDDSkLYGdka9Z0Peg3ZuMTEx\nhCxbS5veM3Rue+zAVmrXqSNbAY3Vy4Np07EnVtaG9xaWLPShfa8xmPzPcA4Y78ef5w4zdHB/vH38\nyOvkJMs4KpWKG9ev0WugPA95QRA4+8d+Vi8LkdROrVbjNn065Zyd8Z45Aac8uhvGS1evU6qAI4Wd\ndG+jC4u272eDr37CMdXKObN+rhtTF66icr4cjGldL83rbz97TT6nPBSReA+fwiIIN7KicJH0jyDK\nTVb0pEuXLo23tzedO3emcmXD53HoTBaJRspNtjbSme1Jp4bUqlqZiUajAeINyZU/r5GvRHWsbXTb\nM1XFxHDxj90ELVuHIAg8f/aEe3du8fjxA96+iS+GYWxqBqKItbUVLb9rTd0GqWfUfvn8iYf3/6b/\nMHmTklLi86cPvHn7gV61kkqGVqvTkhJlquLtPYbmzRrTvmPGQ7t+PrMYMHyibFGQlcG+9O/TS1Ke\nxU/797Nk+Rr6dG7LsL5p62ynxJKVa9jiOT79CyWwYu8hOjZrgJWF/ser7GysWT5zPBt+PkyvoG2s\nG9kFi1QiA167j7HCbbjkMVYdPMPQqbP0nqOcKJVKHB3lXSjpS5Yy0ICgyDrPVTnJ1kY6Md8i3C3n\n3rPcC43EWeUKhQJTU1N27P2VvmN1O5N87dIfrFk0gwKFijLT3R1TMwtyOubHqWBxXGp2oqFTQRxy\n5kkwJB/eveTa+SMcmuFOVOQX7O1s+K51W2rWqZ9wje8cN8ZN9ZbtHtNinqcbAyemnBjnkNMRt/nb\n+XHzQqZNHoevX6DecqxvXr9CLYg6iZLoQmRkOO9ePaZ+Xd3OKD958hTv+YuoUqsxRQo6MeSH7pLH\nXLJmAz981wCrNEo2SkWlUnH8z9ts9/fIcF8KhYIBHb6jTqVydAtazYx29aiVbM/50J93qFGxjORj\nY6/ef8LcMf+3y1gWxSSLsazgSWdVxCx6BEuhUDgAa4ByxKt4DhRF8YKu7f9fGOlvsSdtCO9ZrntI\nrmimVCpZvHQlTTsMT3MRIQgCezcHcfPqBUwtHKhepxn9x+hWYMAxb0FadBhIiw4DAXj76inXLhzh\nlwMziIr4jFoVg3OZcjjlz5iClS6cP32cIiUr4Zg39bPKCoWCTn0n8eDun4wYOojJU6dRuox0YYb5\nvnOYOjsgI9NNwgKvKUwYk7pCmBaVSsVMr7lojK2Z6rOCTSvmMWZgH8mnHMIjI7l98wbTPCfoO+UU\nmRS0gakDe8qaY1G6WCG2+nvgEbKOQ9cf4NnjnzKXq49dYZuX9HtY9dtZJnj5p39hJpEV9qSzKmLW\n9aSDgYOiKHZRKBQmgKSVYtZceshEctUxQ6OtCRsdHU14eDhmZmbY2trKYqDlugeVSkVYWBjGxsYJ\nBTseP37CxwgoWCTlmrlfPr9noecIfKYNwDZvBYbM3Edc1Ad6DZup9zycChSlVeehjJ25kok+W4mK\nFXjzLhSfWZOJiYnRu9/0EASBbZvX0qnfZJ2uL+VSjWnzd7Buw1YWBwUgCILOY104d5rSLhVlE2N5\n9OAejjlsKJ6OSMS2HbsYOm4a33UdzqSZgajjVKjD31GrmvTw5HTPucwa3F3W79Cjl69RmJhQtWxJ\n2frUYmFuxoLJwylfpTKdF2zmc4SS5YfO0KVZXcxMpfkktx6/oHC5yt/UKGbFPemsiqhQfPOf5CgU\nCnugviiK6wBEUVSLohgm5b7+33jSUh6uGRkjIiJeP13uveeMRgMSFxVJfCZbFEWWrFxPr1Ffe3t3\nrp1jz+bF2Djko2GHqeQrHC8NuXPJSHoMmoqZmTzhz6VzR9FvtC8lylTh0b1rTJ80mkqVK9F/yBhZ\n+k/MyiX+tO4yXNLcLa1sGDtzBZdPH2Tk8KG0bN6Mjl3Tz3LetGGNrEeuVgZ5stAv9cjF3Xv38F+0\nlLpN2jJ38baEh3uI7wT83EZLHu/qzVsUymWHc2F5S0ZOX7qFpR7y7m8np0OTulRzcWZwwDLCwsI5\nEpx+AZHkbD5xBe9FywwwO91JSbv7P086ZbLonnQx4INCoVgPVAL+BMaJohilawfZ2pPWkln1nmNi\nYmT1nuVC6z0rFArs7e2T7K9u2rKd6g27Ymr6T7LNzatn8BjbhYsXLtBrwgZ6jFmWYKCfPbyOpbkR\nLpXlUV26e/0cdva5KVEmvthEiTJVmOq3E4d8LowZ2ocTRw/KMg5AWOhnnj55jmv91nq1d63fGvfA\nvYSqrBg+ZCDnzpxM9dqN61bQul032RYyxw/vp07N6inW/v348RPjJk9ny97DeMxfS5vO/8hWXrlw\nggqlCpMvr3RvPnjZKqb365zhuSdm99GzNHStTC4HeQRd0qKQkyPFChUgf5FijAneKGmhfvzqHWo0\nbJ5wNPFbaOenxH9GOnVEhdE3/0kBE6AqsEwUxaqAEnCTcl/Z2pNOHO421JdMo9EQGRmJKIqYmZlh\nkYFM1bTQ5x4Se88pFRX5+PEjF6/9TY+h8TVxY6KjCPIehV3uogyasQsz86/POh7aNIPp87fofyPJ\n5rdjrR/T/HYl+b1CoaBWo45Ur9uGX3ct4ae9fRkzcQYlSpVJpSfd8J09lb5jpFX8SY6RkREtOgyg\nUaue/LwtmK1btjBu4iScnf+ZW0xMDFf/vML8xfJEAgRB4NCPm1m1bHGS35+/cJF1m3eQM09Beg/3\noFDRr9XCftwYxLpFvpLHXLlhC92a1cXaUr7PsyAI7Dx6lu3+7rL1mRYfQ8P4GBnDEj9PLvx5nQ4z\nF7NgWNd0IwOCIHDw2gO8Aseg0WhQqVRA/N/e2NgYY2NjjIyMMmUb7b9wt+4I3yBx7PzFy5y/lKbE\n6kvgpSiK2ov2INFIZ9t60hBvQNVqNXFxcURHR2NnJ9/qXRRFYmJiiImJwdLSMmG1nVHx+9RQKpUY\nGxvrvAiIi4tDqVRiamqKlZVVig+USVM9aNJlErZ2Ofh1z2ounD5G+4FzyVc4ZXnGnzfMwNW1FtXr\nfZehe9GyZuEUqtRuRaUaTdO8LiL8C7vX+hAZ+ha32fOws0u59nVanD11lGvX79JjiLwGIiL8C7vW\nziP0/TNmzJxDbsc8zHGfQseeA2VTTFuzdD7VyxWnaZPGCILAitXruHL9DhWq1aFt1/5YW6fsWW1f\nG0T5Apa0a5n2+5scZVQ0E6bOYKv3BFkN0dTFG2jbtB51K2eOalf/WQtwmziewgXihU7CIyKZ6RdI\nhfw5mdAt9WjK9mMXKNagNa41agL/5JpoNBo0Gg2CICAIQhKDbWxsbBCjrS1NqU34a9WqFSdPnsxS\nkTodyJR60s/v3zH0MOlS2LlcSvWkTwGDRVG8r1Ao5gCWoijqLA6QrT1pLXJ70mq1GqVSiUKhSNh7\njomJSThz/C0RRZGoqCji4uKwsrJKtajI0WN/kLtwZcLDPuPvPpgKtdszbPa+VB80H948ITb8tWwG\n+sXT+0QplekaaABbuxwMnBDImxcPmeM+lfoNGtKxq+6qUYIgsH3zetwD92RkyqnObdAEf96/fcGC\nQB80qghMTYxlM9DRUVE8e3Cb/t3aMNHNg2iVSPM2PfAeMCPNTO2YqCge3TrL9AFzJY85bbYPvVrW\n5+CZyzx98443n8L5EBZJaGQURsbGmJiaxm+PKBRERoRTtmBeBrZrSpF8qYfUX7//RHh0bKYZ6Gt3\n75O/YKEEAw1gZ2tDsO9sdv50gO6eS1g9aSB2Nklrh8fEqrj5JpRu/zPQEP/8UCgUGBkZJUSjEhtt\nlUqVUB8gseGWo15ASiqDmVHH+t9IFt2TBhgDbFUoFGbAI2CAlMbZ2pMWBIG4uDg0Gg0RERE4OEj3\nwBKT2HvWGkDtFyg2Npa4uDiDhaK055nTktvTes8mJiZYWVml+mWOiYlh1Hh3lCoFkZExtB/oh419\n2tWuVs5uwyTvNdjZ58zQfWiZM64j4z03YGMr7W8iiiK/bA/ixYOrzJkXrNP55YXzZlG5bnsqujbS\nc7a64zGyLQWLliYy/BOxMREUL1aCVu06UdJZ+vGtmJgY3Mb2JTY2lhLO5enUaxgFi+imOe03YygT\n+ndOt2CGFrVazYqN2zj4x1lsLc2oW9MVpzx5yOOYC8fcuciVIwc5HOy/2jLRaDTcunuPI3+c5OWr\nV6iiomhQqRR9v2+SRKSkl0cgC6aMwCm3PJ+f9Og2dS5L/H2wSSWy9ezFK2b5BTLku7q0qvVP1vuS\nn47Rsu8IipfQ7X3Tot271hpujUaDQqFIMNpaT1uKty2KIkqlEmtr6wRHo3Xr1pw+fTrLaP3rSKZ4\n0k8e/G3oYdKlWKnSX3nSGeU/T1pHtN6zkZFRipnbmSU9mhLaY1+xsbE6leScMHEqt+484vveHjhX\napRu/0d2zqdxq66yGejd6wNo1KqXZAMN8e9z+14TePTXVcYO68PEaTPTNICvX73gS5gyUwz0+T/2\nU8G1ER36TAFAo1bz9MFNfvv9d96uW0tUZCgO9nY0aNyceo1aIAgCf/91izs3/+TZkye8f/8OhZEx\npmaWmJpZEBkRjrmVPXMCQyTJpD68d5s8dmY6Gehrt+6wdONOjM2taNWmEw5/3mRV4FysUqgjnRLG\nxsZUrlCOyhXia4hHRUVz7tIV3Nb+zKdPn7AwVlAirwNVXEpnmoHefvA4jRvUT9VAAxQpVIC1wf4E\nLl/Drxc2snhsH75EKPksmks20EASgwz/GG2t4c7Ivnbya/5lBjrTyMKedIb4f2GkQX8hkMQGMLn3\nLNcYupDaIkCtVhMZGYmxsTH29vbphsJu3rrDe6UlY3wPYmKafmGFT++e8+HFdfoP36j33BPz+eNb\nnjy4Rce+UzPUT4myVZk8dwdrF06ktHNx+g4aleJ1/r4ejHZfmaGxdEEQBA7tW8u0gL0JvzM2MaFE\n2aqUKPtP/eMPb59z588T+HjNxtjElHwFSpCvSBWaVu9E7ryFkmTZ+09pzwyvZZJ1zNcvnsXK+anL\nWEZFxbBo9Xr+fvIKl4pVmDrbnxw5c7F2eRA9O7bR2UCnhJWVJc0a1adZo/oAvH33nkHjppDTwZ6K\n567QvE51vfvWBUEQ2PvHBdaHpK+cZ2JiwrQxw7lw5RodZgZTNK8jHgsWp9tOFxIbbW30QWuwBUEg\nNjY2YV87seH+zwDrT0rnlLMD2dpIJxczkVpFKrH3nJ4BNPSXK/lZbymLBy1qtZqA4DV0HLIYY2Pd\n/vR7lo1kwpwVGZp7YpbOHc2wqUtk6cvK2pYxM1dz9Od1TBk7CC+/ECyt/tljPPDjDirXaIZDTsNr\nHW9cMpM2PcZgYpJ2lStHp8I0+r4vjb7vm+Z1p4/soEadBtjZS4s27Nu2ivbNG2CbwrbLH2fOs2HP\nfmwdctG+cw+GVHFN+MyEhn7hyd83mTpE+h52WqzatI2pE8dTvVoV1qzfyJpf5jN/TF+KFtCtapVU\n5izfzJC+vSQlVtWqXgUrq9H8fPQ0uXKlve2TEZLvU6e1r631shN/pzUazX/70WkgiP950v9apBpQ\nfQxgZoa7pSweEhO0ZBWVm4zQ2UAf3uFHk9bdcMgpj2LWLzuW4lr/e3I6yvuAbtZ+IGUr1WXy2CEM\nHTGWStVqolKp+P3IIdwXyJ8slpywLx95//YVvWo2T/9iHRAEgfNHtuK3ZKukdjExMdy+cISJQUnL\nhl67dYeAFZtwrdOAOX5LsEnhnO28WZOZPVG64ElavH77ls9hEdStHZ+ENWrYED59/kzA4iUIUREs\nnDQUSxn1wEPDI3n+MQy3Wq6S2+47dBSveZkr/6lQKDAxMUkiLKT1ttVqdUIiakxMDKdOncLBwSHD\nOS8ajYbq1atTsGBB9u/fn+F7yEqIht/6/ib8vzDSoHs9Zn0NoKGNtNaTjo6OTjFxLT0ePHzEg1cq\nGtWsoNP1n94959OrmwwYMTEj004g7MtHbl89x5S50gyPrhQoWppp83ezMWQaZ04d48OHd/QaOitT\nPI9l88bSZ+x82frbFDKF3gPHSD5mE+Q1lmmjByd8Jr6EhjHNN5A8BYsxb9FKrFLZoz114ijlnYtR\nqGD+DM89MR5zF+DrmTTsnitnTnznzOLe3/cZ6LuMaiULMblfxiuNAUwMXMXk0enrmifn/JVrVK5W\nw2AaB7qSfF9brVYTGxuLsbExR48e5eDBg3z48IF27dpRr1496tWrR+3atSU5IcHBwbi4uCQoI2Yn\nhGyqzZU97+p/JP7wpmdEtUeXIiIisLCwwMbGRvID3pBGWhCEhDPfdnZ2mJub6/zlFAQBH/+l1Gur\ne4GBPctGMniifIUhFvuMYOCEAINuC5iZWzBkcjAaY3tu3byFo1Nhg42l5caVExQoWgZHJ3lqDX/5\n+JbYyA9Udq0rqd2Dv26R186MMqVKIggCnoFLcPNfzohJsxk32SNVAy0IAnu3rmHUoH5yTD+Bnw8d\noaarK46pVI8qU9qZZcELKeRSiU5T5vHb6UsZGu/6vYc45nWieNHUi6akhCAIHDpxlnYdOmRofEOh\nPfbl7+/P3r17adeuHX369OHVq1d4enpK6uvly5ccPHiQwYMHZxkFNTkRRKNv/mMIsrWRTkxaRlqt\nVhMWFoZGo8He3l6SAUzcvyHQHvuKjo5GoVDoJTm6cs1GytTpq1OiGMDhHfNo8n132fZyD+5dRbXa\nLcidR14N6NS4fe0CQ9x34D9rOBdOGDakt3fjIjr2kyQglCbrF45h6Fjp5Rs3hsxmyqjB7P31N34Y\n545r4zb4BIRQsFDaC5XAebMYObDPV0erMoJarWbfgd/o36dXmtcpFApaNmvKiiXBXH8bQbdpfjx7\n806vMX3W7mTSyMGS2+379QhdevT8V+z1KpVK8uTJQ9euXQkODubw4cOSnjsTJkwgICDgX3Gv+iCi\n+OY/hiB7/rUSkZY0aGLv2crKCltbW70/wIYId2vPd6tUKqytrfWSInzx4iVX7ryjaOma6V+MNsx9\nm4YtU647LAgC79+80FkHOTz0M9cvnqB5hyE6zzkjbF4+m/pthpOvcFmGzdzL9WvXCPYebZACKzvX\nB9CkbT/MzOUJk968fJxSzqXJ4yRtMbNv60oqlinOiOk+vFEasXDpelxrpu+Jv3jxDLUylDqu1fSd\ncoq4+wYwesRQnReTZmZmDB88AL+5vriv3MHmA0cljbfh58N817RJmkeuUkIZFc39569wda0hqV1m\nIack6IEDB8iTJw9VqlTJll40xIe7v/WPIfh/tyetJbHwh5S95/SQmkGeWh+xsbFER0djYWGBhYUF\narVar368/BZTv8u89C8m3gCv9+tFjXotWbVwGp8/vCMmJgpTU3OMTc0xMTHHyMQUG7vchH16TVTk\nZ3LkyEXj1j2oUK1+in0u9h7OoImBmXK05OO7V7x++ZIWvdoBYGRsTNt+Pjy4cQKP0R0Z576YvAXk\nCUtHRUXy4M5V2v+QsaNkiTm0cxG+QRsktfn88T37tq+hfsMmeAUsxdZWd+nbhb7uLPJcGPl6AAAg\nAElEQVSWVyb14ZOnYGRElUoVJbfNmTMHIQsXsHr9RgZ5BrHSfXS6YjVqtZpD56+zNlh60tf6nfsY\nOmLUv8ZoRURE6F1c49y5c/zyyy8cPHiQmJgYwsPD6du3L5s2bZJ5lt8OmTVEZEOhUDwFwgENECeK\noqRV4f87I631nrXeaXrCH1L6h4wbaUEQUCqVCIKQpKSkPp76lm27KFShPeYWVmleFxUZyr61M7h3\n/RRV6rQmdxFXSuYuRI7cBbCysU/zXPiHN0+4fflXDv20hejIUPLkK0jztj9QsmwVftu3lko1mmTK\n3jDAMr+x9Bi7+qvfl6rUiHzFKrIyaBSutRvQqtOgDI+1xGckvUd6y7b4+HHjfL7v2BNzCV752mX+\nHP11N34LQihXQZoM6e7tG2jZqB65cuSQOtU08VoQzML5+h/jUigUDB3Yn5u379Bpqh9+I3/ApWTR\nVK+fsmgNY4cOkLzIfvPuPQozSwoXLoxarc6S55NTKlOpryc9d+5c5s6N/7ucPHmSBQsWZCsDDaDJ\nuoFhEWgkiuJnfRpneyOd2Lip1Wqio6Nl954Tj6UvoiiiUqmIiopK8J4z0t+7d+84fv4eLXqnfh73\n0Z0LHN4VgJlVTopVaI0mLpquQ3X3SBQKBXnyFydP+zEJ9/D62V+cPbWfrWsW8PLJX8xaaPgjUACH\n9q3GxbU19jnzpvi6jV1OBrpt48TPwfhN78dEz9V6L9BuXT1Nbqci5C/snJEpJxAVGc6Lh38yZETK\ngizJuXD6GDu3rKG4S02aNGsh2UBHRoRz+cwx1gTJe+Ro0649NG/SBIcUymlKpWL5ciwLXoSnrx8V\nCuVmbO+v60E/e/OOWNGIKv9TO5PC+l0/4TZzTobnaUhSCnfLVSQoKy5KMkpW9aT/h96Ty7JLDznR\nigaoVCqsrKz0ytzWBX33pQVBIDIykpiYGGxtbbG0tExRClDXvkVRZJb3Qup3nJ7iWEf3BrN4Rnuu\nnf+d7/qtpFW/Zdw6vZpuwxdJnnvyORYo6kLL7tNQx6npP2UjuzYtJmjOYGKida5xLpmoqEgunfmd\neq2HpTu/xh3G07izG3PGd+XhX9f0Gm/3+kC6DJSe3JUaq/2HM2zczHQfnB/ev8FtTD+uXr/DhLl7\neX7vHMNHSz8i5zNzEu4TRsv6oI5URnHi7EV6dO0kW582NtYEzPPGzLEQvd0DiIqJSfK6W/B6po0d\nIbnf67f/wtmlfIJXKscWVWYgVy3phg0b8ssvv8gwo6zFt87sTiO7WwSOKhSKKwqFQnJyTrb3pFUq\nFZGRkQCYm5vLFt5OCX2MtEqlQqlUYm5ujo2NTaoPCyl9b9m2i/zl2mJp9c8XOjL8M/tWuxEZEY5L\nza50HrsbI6P4xJ6j2yfTsstYrPXQ0k6JYz+GUKFGK4o4V6OIczVeP71D4OwhFCtZhh6D3WVfIIV4\nD6fjoPk6P2gLFq/EYI+97F05AWsrU4ZO8tepUAfAlhU+tOg4GHML/aUzE3Pn2mkKFy6cZuEMQRAI\n9vMgNFxJnwlLyJk7H3vWzqZbj15YWqa9lZGck8ePUK5kUYoXlWdvXsvUOb5MmzjeIMauR9dOuFar\nQm+P+Uzr055alcpx8NQFqlapjGMuaXrgoiiy99BR/BcGyT5PuRFFMcl3JTIyUhYjnV3JwmImdUVR\nfKNQKByB3xUKxT1RFE/r2jjbG2mNRoOVlRUajSZTEkR0HUMQBKKiolCr1djY2Mh2BObNmzf8ceEB\nzXv9E+bev9mL54/+ol57d/IUSFor+sXDS5iZqClXXZ4SlF8+vubh7bMMnL494Xf5i5Zj0Ixd3Ll0\nAM8JnWnWtjf1m8kjYPHn2UPkKehC3oLSQs/mFlb0GreSx3+dx2tSb8pXqUG3/pPSbBP25SMvn92n\n6+DUdbGlcmDLfHzSSBY7/Msufjv4E+16T6VMpXoAfPn0ltA3f9G4qTSFMLVazb7t61i/WL7z7wCn\nz1+kaNGilCheTNZ+E1OieDGWLwnGL2Ahh89f5+ajp6wLTl+fOzk/Hz5Gp67dk2Se/1s86Yxkd/9/\nQPMNwt1XL53m6qUzaV4jiuKb//33g0Kh+BGoAehspLN9uDuxMpehjbSuX3SVSkVYWBgKhQJ7+6/L\n/6XWd3rzF0WRWT6LqN8xvp74w7sXWOTWGjvH8nQaueUrA63RaDi/34tOg+VTy9qyaBhdhgen+F6U\nq9GGobN+4tWr93hN6Mzj+zczNJZarebnHSto0WOG3n0UL1ubobP2YZ27DO6jO3Hyt92pXrt03lh+\nGOWr91jJ2b3Wh/bd+mKRgld+69olJo/8gbefYpg078cEAw2waeFIJk6VHm6f7+nGhOGDZD0TLQgC\nKzduY9Rwwx+xszA3Z47HdO6/+0JoZCzhEZGS2iujornz8Cl169VL/+IsQEqJY/950qkjiopM/6ni\n2oBBo2Yk/CRHoVBYKRQK2//9vzXQArgl5b6yvSetJbOMtC6qZtq60/o8LNNa9W/YvJ3ClTqCwoi1\n8/piYetEp1E7MTNPOST628YRdOg/O93sb105sMUH1ya9Uk3eAjA2NqFR+3HUaNqfw9u9ifjiz/Bp\ni/Uqg7nMbzTf95mdblGL9FAoFFSu05EKNdty9uAKZo7pTPeBEylf5Z+zxpfP/kbhkhVkUxYLD/vM\n22e3GTn2HxU4QRDYsXEZVy9fpIRLTYZ7bMTaJmkS1oU/9lC9WmXyOknTP7939zbWplCtkm6ysLoy\ne34gw4YMxNyA20iJ+fTpMxhbMG/hcsZ5etDluwZ0aNVCp7brd+xl+KgxBp6h4chIdvf/Bwyl+JVB\n8gI//u+ZbQJsFUXxiJQOsr2RTkvMxBBjpTaG9ly2qakp9vapH2tKq++0eP36NacvP8HcLo5ftwfT\nqIsneQqmnvX64MZh8jg5UaxMLUnzSI13rx7x7uUDvuupm4dnZWNPxyEL+PDmMQvnDKNVh77UbNhW\n5/Hu3DiHqUVOnUVadMHY2IQGbUdTs9kAft89n72bFzN0kh958xVh/44VTPWXL1N9bcBIxkyKD5u/\nf/uKlYvnEh2jpm7zXkyYOzXFfXu1Ws2F39axeMU6yeOtCJrL8gBvBEHg46fPPH3+ghevXvPq7Ts+\nfg7lS1gEEUolpiYmNKpdna7t26Sbv/H46TOiY+OoXUN6QQt9cfeax8Tpnjjly8/CJWtYuzKEo+7e\nBHlOTzOv4NnLV5jZ2FOo0NeyoVk13G3I7O7sSFbckxZF8QlQOSN9ZHsjrSWzqlSlpmomx7ns1IqE\niKLIyHHTeP0+ktJVC9B13O40HzqqmChu/LGUUd4/6T2X5OxYOob+U6UXz3DMV5whHnv4dfNsrl74\nnWFTgtJNLBMEgZ1r5jNk5t40r9MXc0tr2vT1IvzLe7av9eTx35eo06STztXD0uPm5eOULFmSRw/u\nsnCeB7mditKmzyycCpRIs93GhSMZMWa8zkpegiDw895dbN+6nkKFCjFzwQqMTU2ws7PH0TEvufM4\n4VKkPDly5MTBIQd29g5ER0Vx8fxp3OYvIfTzJ3LYWtGjw/e4Vv36OeO5IJhAP/nC/+lx8vRZSpap\ngFO+eEU2IyMjhowYx+0b1+g9xo3Z44biUibl3IQNu35ippdvljXIKZH8WfKfJ50232JPOjP4z0jL\nPEZiDKVqlpxZnvMIi7Gh3dClWNmkHzb+df0gug4PyHCYWMve1W40bDMCa1v9hDGMjU1o19+Xe9d+\nZ864Doz1WE7uvKlLY65aMJGW3adhZi5PhnVq2OXIQ9MuUwldPQ01tiyaMwJVdBgWFpZUrduC2k06\nS1p0qdVqnvx9ndULxlGgUEmMrQowavZWnbYbnj64ib2VgvIVq6R77eOH91m1YglxGijlUo1SpUoz\nNyBYpzna2NrStEVrmrZoDcDLF885cfwwG/YeRBkRRjnn4vTr3plffjtKqxbNZTkTrQuCILBuy04W\nLln71WvlK1UhIHg1AfPmUDTvWSYNH5Dk9TMXL1O9Vh0UCgVKpTKh0pS2bnPyLOqsROJnSlxcnEFP\np/zbyeLnpPUm2xvpbxHuTlyPWm5Vs+T38PTpUx69NaLt4K+VtlLi6vFVlK1Ul/xFXGSZ09P7V4lS\nhlG+pu6h6tQoU6U5BYpVZnnACOo1aUvj1l8XaHh87zpxGiNKVmiY4fF0YefSMXQbvRZbh3+KjYR9\nfsvjO3+wfP5kopWfQVDjUqk2rg3a8Pr5A57cv8m7V08I/fIRI2MTTEwtMDYxx9TMimcPr9Kp33Tq\nteglyaPbt9qNBUFLU31dpVKxbvUy7ty+Q9GS5ek7yhdHp4LMGd8Rn7nSs6C1FCxUmB/6xSeFqdVq\nbt28RsDqbVy5fJFRQ/vr3a9U/BeF0LPvIExT+S5ZWVsz2yeAg/v38cOYaYR4zyCHgz1qtZrfz1zC\nf2FQQrlXbc3m2NjYBE13rYdtbGycZTztlLz+rDK3rEh29aQV6Riuf4eobRoIgkBcXFxCsQoHB3nO\nAqdEdHQ0Go0GjUaDkZFRQlEMuQgLC8Pa2jph702j0dBn8CQqtV6AqVn6cpJhn15yas8Uhs3cKcuX\nXa1WE+LRlqEeezC3lFbcIC0EQeDo7vl8enOPcbNWJbyHgiAwZ1xHBrnvwsLS8GG/U7+uQtCI1GqZ\ntkhKTFQET++d4/n989jnLkyuvCXJmbco9rnyJwmRf/nwkmM7pzN61gZJ89i7zpMalYrRpHmrr167\ndP4M27dtxsLKgSate1Kxev2E92vvpiAK5rWhbQd5jrtpmTxuGCMneHD+zHEunj3O1LHDcSlTRtYx\nEvPh40c8AxYz1z9Ep+vfvH7JfJ+Z9GrbnE+hodRt1pry5cuneK12Qa1dAAuCgJGRURJv+1sZxsjI\nSKytrRPm1rp1a06fPv1vNNQGn7BCoRB/vxGT/oUGpnklC0SZXfps70lrMbQnLYoicXFxqNXqBO/Z\n0F+mwOCVFKo6WCcDDXB400gGuW2QbV6bFw2hbZ/ZshpoiN9rbNF9Oo/vnmP22PYMn7KQAkVKsTHE\nncYdxmSKgY6JVnL70iEGTN+X7rUWVraUqdqSMlVbpnndz2tGMcxtmaR5fHz3krC3f9Fk8sgkvz91\n4ig7tm+jco3GjJ25EhvbpGHnL5/e8/iviwwfKm289Pjt4C+4VKxGoSLFKFRkEK3adWXtskBC12zC\nZ5Yb9gZIbHL38mOKu4/O1+fLX5DAkDUEB84FdTTDUjHQEP9cUCgUmJqaYmJikmCoNRoNcXFxxMTE\nYGRklMRwZ0ZoPLVn1b/QQGcaQjb1pLO9kU4e7jZE4oharUapVCKKImZmZpibm8vav5bEC40bN29z\n56lApaa6JQ4e3+VGk/bDsHOQp0b09XO/kDNPEYrKlB2eEsVd6jDAbQebl42mYOEihIZF4FL9a2/S\nEGxdNITv+86T7bNy+fgmKtdoQo5cTpLabV40Eq+5fgn/fvHsCQF+vjhXqIVHwHZMU6kRHuI7kllz\nfGT9rMfExPDr/p8ICFmf8DtbWzvGT/Pk2dPHuHn5UzS/I1PGj5bNkB374yRlyks/cmZsbIyFuTlT\n3adJaqcNeWuT8xIbbbVaTWxsbJJrtJ62oYznf0ZZdzRC9nyvsr2R1mKID7soisTExBATE4OlZXwS\nkz4lJaWOGRsbi++CtdToqJu04fMHFzBRxFCpdjtZ5hATFcmpg2sYNit9LzOjWNk40G/KZuaOrUfO\nXE6oVSpMDJw8c+/qMXI5lSBvQXlCuCpVDHcu7mbqfGnv1/GfV9O4cUNy53YkKioKXy93jE1tGTtz\nOfY5cqfa7uDetdSrV488eaUtCNLDa+ZURo6fnmJ2eZGixfFZsIILZ0/Qf+REurRpSbs2GVtQCYLA\nxh17WbRU+pGzO7duUKZ0CXLmTD+RMq2Fe0pGW1sLQFsPAPjK05ajXG3iPlQqlawiNNmRf0nFUcn8\nvzHSkPoRJn3QaDQolUoA7OzsMDY2RqVSGTSkrp2319wgnOuOS9DeTgu1Oo4L+30Y5fW1gfjy8TUv\nHt3gzfN72DrkoUbj7jppWK/370eXYQtlO5KUHj+tnUGDdlOxy1WYxR7t6TDAi+JlDXM2VxAEjuwJ\nZMD0H2Xrc9/yYfQYMkeSdxkdFcndy/sJWrqGVcuDuXPnb3oPnUGxUmlXfIqMCOP6+UMsWqJbIqGu\nXDh3GqcChSnpXDbN62rVbYRrrfrs2baeASMnMG38CMo461ctzMd/IX0HDZdsnARB4LcD+1i0UF75\nU/gnPG5kZJQwL62nrQ2Ri6L4VQZ5Rp85/x2/Sp/smjiW7Y104i+HHPvSWk82OjoaS0tLzM3Nk4xh\naCN96sx53kbno5xTyXSvj4mOYLNfKywsLFnp0wtjE3NMTMwwMjHD2NgMK5vcOOQpgq1jBaIi3rNx\n4SiiIz9haW1DjcY9KVe9+VeG5dhPIZSt2pw8+dMfXw5ePb3Dl8+f/o+9s46LKnvD+PfODJ0KggIK\ndteaa/faHdi6dufa3d3u2q7dXbtrd3c3BiIGksMwzNz7+4PfjCADzMCg7Orz+fBxlzn3nDNMPPd9\nz/s+Dz83qAtAkz5bObppMHcvH6JeO/NpaOuwfekgqjT+DQtL8xxZ+D28hIurCz65TNMzWDWjM6V+\nLkuPLh2p3aQTDdsn7ZIFsGBiDwYNNW6ssRBFkbV/LmfWwj+NGi+Xy2nRtjO1GzTjj3lTcbJVMGJw\nP5PWfPnqFcHhUZQsVTbpwV9g366ttGvbyuibopTeuOvOrGOT9pcV5DqyNrYY7cs9hYWF/SDpJJCW\nW7AEQZADV4DXkiSZ1Arznyfp2EgpSeuiZ0mS9NHzl/OnJsLCwliyei8/N0k8zf3qyWXO7ZvJ+7fP\nKfxzfcrWGYiVEcVWhcr4AhD84RVPbh7kwtHOqCI+4eLuRdlanbB3SM+zuxfoMHS9WZ5PUhBFka1L\nBtOox0b97yytbKnV4XfuXdjMolEN+HXYWmztzdOrG+j/FJUynBwFK5tlPoBj28YxcPJmk645eXAd\nL54/Ile+ooydsxWFkZHk0YObKVqkEJmzmNfhavK4EXTqPjDB9qeE4ODoxJAx0zhx5BAduvdjzpRx\npE9vXC/9uKmzGDvZdOvUkOBPvA/0p1ixziZfay7oSFuXlfoyPW5MBbkh3e4fJJ04tOK33kGi6Afc\nA0wWX/8uSDp2mjs5JB07era2tsba2togIad2BfmEqQspWG24wbVFUeTiXwt5dvcEGbyKUrDyMO6d\nnkHlJqZHVc6umSletRvFq3ZDkiTe+T/g2tn9XDm5hWx5iqHVao22dkwJti8bRKkafbG2jV8xnK+0\nL5mylWLppNZUbdyLQiVTXlC27Y9+tOy/NsXz6PD3xjHUaNgZayOr39UqFUtn9CDQ/zEzlx3AydnF\n6LUiIsI4f2Qr8xavSO52DeLunVtYWFlTqGjxZM9RqVot8hUozMDRw2jZqC6/VEv8Jmjj1h2Uq1id\ndOmNf/76a9euYPDAvsndaqpAEAQUCkUc0k6qgvxL/HDAShppURYUQBAEL6A2MBkw2QA+bcrspBKS\nQ6KiKBIeHk5UVBQODg7Y2NiYxfPZVGzeuhuZa3kcnOMWA4V+CmDXkk5snd8KubUnVdqso3CV37j+\nz1jq/bowxdG9IAi4e+Ul5OMbavhOJF+pNvw+pjGnDyxL0bxJ4eWTGygjoshWMGHzhHRuWWnWdzu3\nLx1n44LeemGK5ODvLdMpVrE1dg6mG30YQvDHN4R8eELxCg2MGr9vw1zmjG5HSNAH+g2bbRJBA8wb\n34XBw0abtT1IFEUWz59Jz/7DUzyXW0YPZixYzeW7zxg+bnKCr5VSqeTIyXM0adHG5DXu3blFrhxZ\ncXEx7W/3taVCdcVolpaW2NjYYGdnh5WVFTKZDI1Gg1KpRKVS6TUe/Pz8CAsLS7YD1qtXr6hcuTL5\n8+enQIECLFiwwMzPKG1AK377nwQwF/gNSNYX1HcRSScHkiShVqtRKpVYWVlhb29v1Ac5NUj61avX\n7D58k5J1J+p/F/DiFse3jcXOyYt85frjnOHzGfHF/cMpW6cX9k5uZln/ye1jICjIXijGc9ozZxlu\nn1nD/BF1qd1qODkLmH5umBhEUWTHiuE07pV0mliusKBK86k8v3OY+cPr0H7wctJn8DJpveCgt7x4\nfIO2g4ckd8vxsHtpd7oN/yPJcXeunWDP+rkUr9SWsnWK8+7RfnLmS1r6MzYO79tIsZ9+Iou3ef2c\nZ0+fSKsO3bGxNU8fvFwup0e/YVw+f5p23foyffxIPD3itlYNHzeZ3gOGmkyaoihycN925s42f7FY\nasNQBblardYfr9WqVYuoqCg8PT3JkCED5cuXp2DBgkZruFtYWDB37lyKFClCeHg4xYoVo3r16uTN\nm3gR4L8NabG6WxCEusA7SZKuC4JQKTlzfBckbWq6WxRFIiIiEEURBwcHo1O7qXE3Looiw8fOpkjN\nGM9njUbNvhU9EOS2lGu6BCubuKng149OYmdnSc7C5uknVquUnD0wl2b9PjtAyWQyClfoSN5SLTi3\nfypHd8zFt88inNObp+Vn6+/9KFN7EFbWxqf3shaojluWImz+fQBumTLTuPM0o6PKjfO606THH2Z7\n/c7/tYzi5Wom2hP96eNbVs7qh1vmArQbsh25wpJ1U2szfp5p59fh4aFcPL7d7Gnuhw/uEamKolQZ\n88uvlvi5PDly52Pc+CHUqFSGZo1iWgOvXLuBq7snOXLmNnnOfbu30a5NK6OJSwfd90Fa6kfWVZDL\n5XKcnZ25e/cuK1eu5ObNm9y6dYvFixdToEABtm83zpUtY8aMZMwY8160t7cnb968vHnz5j9H0t+i\nT/retRPcu34isSFlgPqCINQGrAFHQRDWSpLUztg1/vOyoBAjTK8jXrlcjrV1wgpdarWaiIgIrKys\nEk1tG4IkSXz69Mmo3kxjMX32YoIsKuDuXZTrJ//k9vmdFKsxHFfP+NXCalU4Z7Z1otWgHSgSELkw\nFZvmNqdS4wm4eCT8xRkS5M/pXWOxsbWhRc8FKTqvfvrgEmcOreOXNsb1gBuC392jXPxnIUV+rk2l\n+j0SHXv64HKi1dGUqdUz0XHGIjIilO2L2zN4qmEnMlEUWTP/N0KCg6nZejLOrjFGIjv/6EbDZr7k\nK2yaOMzk33wZ9Nswsnj7mGP7+j326tqeqXOXY5eK56CSJLFu5WJePLnDrElj+bXnAGYtXI61tWnG\nKcGfgti+aTUTxo9N1h7SYlGWrp1TJ4y0fPly3NzcaNOmjf7x5HgC+Pn5UbFiRe7evfs1n/NXkQXd\ncPrbV461Li9LUBZUEISKwOAf1d2JILFIWhRFlEolGo0Ge3v7FAkHmOuM6+rVG9x/LccrrzPrZzTA\nK1dVarTfhJBAhHh2Zw/qtJ9jNoI+f2ghWfNVSZSgAZzSe1K30wr8n17k93FNKFiyBpXr9zJ5PY1G\nw94/x9Kk99bkbhkAn/xVyZK3MnfPrWfesDpUadSbQqXiZxaU4aHcuXSIDsPMZ3m544/OtO09Ld7r\nL4oih3cv48qZv6nceDDZ8lXQP/bswQXSOVmaTNBH9q2nePFiZiVogDkzJ+HbrkuqEjTEfB7bde7N\n3ZvXqNu8PY2bNjeZoAE2rFnGsCGDkrWHtGpdaai6287u87FDcgg6PDycpk2bMn/+/DR3U2IO/EsU\nx0wOfL+LwrGknLDUajUhISEIgoCTk1OyCdqcH3alUsnUeWt49fwhx7ZPplyTReT9uUuCBH379AIK\nlKyLS6acZln/Q8BTXj65RNHKXY2+xjN7KZr13YFKJWPJ+Kao1aYJ3q+f14WKDcdgaZW0dWNSkMlk\nFCzXjiZ9tvH47jUWjqyPv9/dOGM2zOtCvQ4zzfa63b6wl+y5C5LR63N9QHDQO5ZM7c7sUW0R5S50\nHLE7DkGLosip7WPp2HucSWuFhwZz8eQuWrfrZPBxURQJDAjg5vUrqFTGvw5PHj8kIkJJmfJVTNpP\nSuDilhFP75zcuHWf1cuTPsePjevXLlG4YH7SpUueTWpahSGSTm7hGMRkE5s0aUKbNm1o2LChObaY\n5iBJ3/4n8f1JJyVJMln28buLpGNXlUqShFKpJDo6OsXRc+w1Unp3LkkSLdt24YnfJ0rUGIp71jKJ\njn//5h6RwY8p6jss2WvGhiiK7F/dh0Y91pv8PARBoGjlrnjlKs/iMY2p334s2fOWSvK6Wxf2YePg\nhUf2ksndtkEoLKwoU3cYkeGfOLp7EpFhb2nVZxGPbp/EM1tRXDNlN8s6muhorhxdqpf+vHr2AEf2\nrMYxvRdl6gxKUGJ038q+tPx1ANY2xt+Y+L96yqTf2uDs7MyAPj2QKRTI5QoUCgvkuh+5AgendDg6\npWfn7n2EBL3D2cmRRk2bU7hIsQTnnj1jElPmpG7l/peYNmEE/Ub/TjoXN/7Zs46+PbsydcZs7OwT\nJ6Xo6GiO/XOAeXOSb8X5b0F4eHiySVqSJDp16kS+fPno37+/mXeWdpDG+6STje+OpHWRdHR0NBER\nEVhYWODk5GS2aMocgimr/tyISpGX2p0HIUtCelPUaLjxzxhaDUxZijg29q/uQ9m6g7GxT350ksEz\nL037bOXo5iHcu/wX9dolfF4YpVJybM9SmvUzX9r5S9jYp6N6q9l8evec9Qv78erJdeq0GY9GozFL\nz/fOpd1o1H4Ym5aO4bXfI3IUqoJv//VYWSdcGf3q6Q1sLKMpXCLp4iy1Ws22tfO4f/san4LeU72u\nL41adjda6ATgzavnnD2+j00bN6OMCKFgoUI0a9EaZ+eY13nezCk0b/Ur9kmQozmxffMaSpSvRTqX\nmE6EGg3aUuCnsgwa2J/WrVtTvmLCEf22zWvp0a1Lim+I/w3p7pT0SZ89e5b169dTqFAhihaN6RyY\nOnUqNWvWNMte0wrSYnW3OfBdkHTsdLeugEytVustJc29VkoEU548ecr+Y48oUqxp0D0AACAASURB\nVNU4ycszO7pTs/VkoxTFjMG9K3uxtkuHd96Uq25ZWNpQs91C7l3YzOIxDfl16Dps7OITwJ8z21Pd\nd8ZX0QJP55YVSYTqLecQ/CmAjQt6oI4MRi6Xk7todYpXbImltXFRrSiKfAz048qJjTy5fxlRlChV\nvQtVfX9O8otfFEWObhrG2NnrEh135fwR9m9fjaWNIz9Xa0nJal3YvLg3Tdv2NplcPDJnpVm7GKGP\n6Gg1d65fYPHiJXx85482WoUgyOg12PxSqwkhPDyUs6dPM2b2pi/2mY1xc7aw9o+JHD92hFFjJ8Wr\n1H/j/xpBVJMnFX2s0xIiIiJwTKYNaLly5VKkIfBvwY9I+j8AURTRaDTIZDKcnJxSzRc2OYIpERER\nREdHM37aUnL8bJx37r0Lq8iatxSZfEzrq00IyrAgrh5bRdO+28wynw75SvuSMVtJlk5uxS/N+pO3\naFX9Y2cOrcQze5kki9PMhYfX9uOcIRs++ar8f2+tAYgMD+L149NsXzYEVcQHRDGarHnKkMErNwF+\nt/n07jlhwe+RyRTIFZbIFVbIFFbYOrjz9O5h+kw+ioOz8X3p+1b1w7djP2xs499cfXgXwLqlUwgJ\nCSFngbJ0/G2lXvp0/sgGDB4zL8XRn4WFJUVLVqBoyQqIosjQHo3xzpabEYN7MnzsVBwczCO1mhgm\njvqNzv0M22nKFQo69hnPjcsn6d65A6PHjidzrD7wLRtWMmXShBTv4XuIpL8X/FfvQ74LktadPUdF\nRSGTyVL1zW7qBz52y9fMuctIl7szCsukK1yD3z8j2P8C1fskHomZgu2/d6BW+0WpEtGmd8tGsz7b\nOL5tBHcv/0XTrjMJ/fSOG+cP0aS3ab3ByUV0dBRXji6lUc/4/aU29unJWbQBOYvGKISpoyJ48/QC\n7wLe4OxRiiwFmuLg7IFcETe9fHzLABp1nGwSQb94dAV7ay1FSlaK8/sbl0+yff0fZMiUlUqN+uPl\nky/O4wc2TqdKjQa4ZDCvBeWyuaNp0qYPxcrWwP/FEyaMHoG3txc9+w1NtRvZU8f+wTtHQTy9Ezdq\nKVKiItlzFWLutIEUK1qI1u06cuLoP9SoXk1vD/s9IC22iaU1/CDpfzF06j12dnZERkam6lqmCKbE\nbvk6c/YCDwOc8CmatMCAKIpcPvAbvv03mS0K+GfTSIqUb4uTS2azzGcIcoUF1VrO5PH1vSwYWRdR\no6X2r8u+WiSzf0UXKjSamOQ5P4CllR0++aomOibA7zrW1jKyF6hk9B5EUeT41pGMm/PZNCQw4BW/\nzxyKV9ZC9BizEUur+OQT6P+cdy9v06m7eS0oHz+4hUqloljZGPlVT+8cDJu2lqvn/qFv9w40aNSM\n6rVMautMEhqNhq2b1zNuzhajxjs4pWPYlFXs37acfr274pPZg2lTJ6PRaIxylPo34stIWmd/+QMJ\nQyv+Nw+lv4sWLJ2sp1wuT1UDDDCOpKOjowkNDdW3fIWFhTF/2T68ixgnQnNuVx+qNRuDjZ2zwcfD\nQz8QEvTG6D0/v38GlTKUPCWaGn1NSpCzaH2c3PIQHBzM66cXv8qaD6/tx8k1Kxm8CpplPlEUuXhg\nHHXaTTPput3Le9K682CsbWxRq1TMHt+LNUtn0abfYhp2HGuQoAE2LuxNr6HTzbF1PURRZOWC8fza\nb3K8x4qVqcGYOdt4+eYD/Xp04NnTR2Zbd9r44bTtPtKkojdBEKjXvCsZPbLSrWtnBEHQF3/qsmQa\njcbkz3daTXd/iX/LPr8lvnX7VWpRy3cRSetk9lLbpUqHhNaQJInIyEiioqL0RWuSJNF/yBR8Shqn\nV3z58HQ+vn3E1ZNrObV3DpIkIpdbIlNYIJNbIpNbYGXtjIRIePBrtJoofPJWoHjlDgbdpNQqJSd2\nTaF5KlZWf4nAV3cJ+/Sehr3/4saRaTy99Q91Oi5OtdSqRqPm8pElNO5lvud4cscQqjUZlGj19pd4\nevcM6R0tKVisHBtWzODB3Zs0aD8K7xyJe01vWz6CBs074uhkPiU7gIXTfqN5x4EJanPLFQoatu5L\nlbpt2LBkElHKTwwfMwVbu+SnXe/dvoHcyp7c+RNuA0sIj+9do3D+bHGKxRJylIrt35xa76vURGxS\n/hrfWf8FaLXfegepg++GpHX/fo1I2hA0Gg0RERHxitbmL1qJImMDrGwNR8Ux16q5dmQGb56cR25h\nSblG07BzzIidoxsKi4QlTgGi1UrePDnDwfUjiQx7h9xCQd7iDSlYugkymYzti9vzS+vZWFgmPo+5\nIIoif60fTNXWa5DJ5PxUYyQBz06xfnod6nVeQroM5vVCBti3rBMVGhuX5jYGgS9vYSGLJmfhakZf\nI4oip3dPomaD1gzv3ZSKtX+lT4tRSd6YvXhyC43yA2Uq1UnptuPg7s2LKCysKFisQpJjHZ3S02Po\nHF48uceoYYMoUqQw7TqZLqMqiiK/L5jNqJkbTL5Wq9Fw8tA65s2cRHR0NBAjWGPInEJH2hqNhqio\nqDhjviTttBihJvQdldb2mdaQFrPdgiBYAycBK8AS2CNJkkm2ct8FSesQ+840td7wX94ISJKESqVC\npVJha2uLpaWlfu0bN25x5kYo2UsZloP8GHCfa4enAwq88jbF8tVVfumwClt7V6P3Y2Fpi3e+Gnjn\nizlzVIa95/XDI2z/vStvX98jvZs3rh5fr41l/8ru/FR1CJbWn1uxMmWrQDr3Avy1fhC5i1Tnp8qG\nVbSSg4fX9uPslh03r0JmmU8URc7vG0PHYcadp+qweV4bwsPCePnqLX0n7UShSDrVK4oiO1cMY+zM\nP5O5W8PQaDSsWzaD0bNMK9jzzpGPETM2cGTvWgb16cSk6QuxsTVehGXejIk0btPHJOEWHQ7uWEbv\n7r9ibW2NKIr6H4jRFtCd2ZpK2pIkpdlI9UckbRpEbdr7O0mSpBIEobIkSUpBEBTAGUEQykmSdMbY\nOf59eaAUIrWj6djza7VawsLCiI6OxtHRESsrK/0HLzw8nHHTV5O1RNyIRBRF7p5bxcEVzXlwcSN5\nyoyiaI05BDzZR6mag00iaEOwdchAruItKVC+By5uOfDKUYn1M+rh9/BciuY1Bvev7sXCJgPuPvFv\nSqzt0lOl1SpCgoLYvrgNGo0mxeup1SquHFlKyZrmUWIDOLt7FJUb9Mba1jjBD5UynD/G1UXURjNo\n+l5q+Q4yiqAB1s3tSZvOg7A10FueEsyf1J/WXUdgaWV69kQQBKo3aE+7npMY3K8bN65eMuq6p48f\nEK6M4qfSpsuNvvX3Q64Jxsc7i17jAGL0qy0tLVEoFMjl8jhpb12xqI68Y3s3W1tbI5fL9WM1Gg0q\nlUpvxPOtSfHLICIqKipRU6AfiIEoffsfQ5AkSfn//7QE5ECQKc/ru4ikY7/hv0bKWxRFoqKiUCqV\nWFtbY21tHS9yHzh0Cl7FBiOTxdzxa9Qqzu4ZQmRYEB45a1O89hJkspiX5/XDfbhmzIJHjqRTk0bt\nT6PhzO4RVG+7FktrB3wKNubm8dlcPDSP2h0W4OBs3hYfAJUylCtHVlC9XcKpTkEQyF++Nx/8b7Bx\nZj2qt5pOJu/kR8D7lnemYtPJ8dqmkov3/g9AG0qeYrWTHCuKIn9tmsCrp7cRo8PpNXa7ScYnd64c\nwSW9IwV/SlwS1lRcuXAcx/Ru5CmYMvlVr6y5GDVrMyvnDefsqWP0GpD4jdC8mZMZNnWNyetIksTB\nbYuZN2MCVlZWeq0D3fkzgEKhQKFQ6Gs8IOYGOalI28LCApVKhSAIyGQytFqt/gYgdnpcV8/yrRAW\nFpYi3e7vBdo0GEkDCIIgA64B2YE/JEm6Z8r13wVJx8bXIGmNRoNWq03Qi3rZyg2oHSqTzjGmt/bu\nuRU8v/M3eUsPxMktf5yxyrC3vH9xkDqdNsabJ7k4vKErpWqP1aecLazsKF5zDGGf/Plr/VDs7B2p\n0WauWeQyddi1pCM/159m1Lmwq2cRqrRZy9l9w8iUOTdl6w0xeb07F7aQwTM/rh75kx5sBERR5Nye\n4bQfsinJsTfP7+bswWUUqdSF928e0bTnPJMIWq1ScXTnPCbONd9rDhClUrFj3e+MnmOevnRLK2t6\nDJ3L6X920Ld7eybNmI+jY/zaij/mT6d2407Y2ZuumHX68HZaNK6jjyR1xGllZaVPZWs0Gn00DJ9J\nO7YWv46oddF27JYmQRCwsLDAwsJCn/7WarVxSFtXhKY7005N0jYkZBLbAesHDCOtngpIkiQCRQRB\ncAL+FgShkiRJJ4y9/rsh6djknFokrVar9Xfmjo6OBj/Id+7e468z/uT8uTkf3z7gwt5ReGSvTql6\nKwzaG945MYwa7ZYl6H5lKm6fXU0Gr8IG/agd0nlSqcUSAl9cYvPcpuQpWovi1bqleM2zB2aTJXcN\nHF2yJj34/7C0sqdC00U8vrqejbMaUrnZBKOjapUylFtnN9Gwh/n0zE/vHE7lhn2xsUuYaN4HPGXX\n8oF4ZCtNo17beXx9Lzly5ydLdtOyASumd6DbgAkmtSgZg1njetGp30QszGRlqkP5Gk3IVaA4I3/r\nT8s27SlT/rOkrP+rF/gHvKNl97omzxsW8ol3L25RubthZbGkzp9jk7ZcLo9z06mLtLX/LwmOjo7W\nk69MJkMmk+lJXjdOlx7XEfzXIu0fQibG4Vv0ST+/d5Ln904aNVaSpBBBEA4AxYETxq7x3ZC0Dqnx\nYYrtpmVlZYVWqzW4jlKpZPSkZWQtO4ETW3ohSQqK1piLpbVhCcZ7p8dRono/7BzdzbLP4PfPefXw\nBFVbr0x0nLt3SWq038jTa5tYP7M+5eoPxSd32WSt+d7/If5Pb1CxxdJkXZ+zWBuy5KvH1eMziQx9\nQ63287F3Slzda+/yTlRpNkN/lJBSBPhdRyFXk7voLwYfV6tVbFvcA0mwonrbJdg5uKJShvLsxiYG\nTI6vbpYYTh/8k0KFf8Ine9KiNqbg6KFtZM1ZEO8c5sksfAl3D29GzdrMmsVjOXfmOIOHxxDrjMlj\nGDQheQIsezbMY+zwfkaPj03autT3l0VjEEPagiCgVquxsLCIMzY2cX8r0v4ykv6R7jYO0jdQHPPJ\nUxGfPJ8Nck7snBjncUEQXAGNJEnBgiDYANWB8aas8V2StDkjaY1GQ3h4OAqFAkdHR33qzRAGD5+C\nksz8vboteUr3x9k94QjL//HfOLm44JXbPL6+oihyYmt/qrReadQXiCAI5CjWCu+CDblxdAa3z6w3\nuZdZFEUOrR1A5VarUvSlZWXjRMnakwgNeslf64ZgZWNDrfbzUSjiR4RXji3DO3dFnN3MY0GpEy35\ndUR8shVFkaPbZ/D8wSXK1BuJW+bPr+fh9V3o0G82MhNUokKC3nHn4t4kTTdMRVhoMCf+3sWoWUmn\n6lMChYUFnfpP4fKZQ/Tu0obcefNSuZZvsvq7b1w6Tuni+XBxcUn2fr4kbfhcL6JWqxEEQS+AokuR\n6xC7glxH2rEJ+0vS1o2LiopCFMUUkbYhL+kfkXTSSKNn0pmANf8/l5YB6yRJOmrKBN8NScf2eTYH\nSX/ZWmVlZaVfxxAWLl7OwUPHyF6oKaXqryDmNTMMlTKIwKc7qdPFfF+qx7f05qdqg7G2Nc1+0sLS\nlhK1xhHw9BQbZtSlXuelOLsaJx26f2U3ilYdjJWNecwaHNNnoULzP3j/+hpb5rXEK0cxytcfpr9x\nCA95x7PbR6jX1XxnuSe2DqBG86FxREuCP77h4PrRREaEk6dEUxr0GBjndb9+fAnFylTDzSObSWv9\nOasLg8bMjXMjpFSG8/b1CwLfvuJ94BuCg95jZ+9ErUZtsDVgzmEIM8f2pNvgGV9N1KNEuVo4p8/I\njDHdaZPNdPMXVaSSW+cPsHDeDLPuS5Ik1Go10dHR2NnZoVAo4pxpq9VqfVScEGnrImiIT9q68bHP\ntL8kbd3Ztimk/YOkjcO3rso3BEmSbgM/pWSO74akdTAHSWu1WsLDw/WynrG//AzN//DRY9ZsPkW5\nxmuwsk06qrh97Deqtl5ktnTtwyvbcHDOTMasya8UzpS9As7u+Ti0dhD5StSjcPm2iY6/d3kXVrYZ\ncff5OdlrJoQMXj9Rre06Xt0/yIaZDShasTUFSvuyf2U3qrZcYLYjjZePzmJnb6PX5r5xZgeXjq3F\nMX0WilYdiEvGXPGuCf30ho+vztDShEK/O1eOs2X5aBwdHFkydzxyhQKZ3AKZTI6VtR1O6TLg4OSK\nvbM3OTL/hDLsE7/PnkDop0Ds7e2p1agNBYsa/jvv3LiEEuV+wd3D/CIxiWHtH5MZPucQpw6uZvqo\nrgwa97vRhYh7Nsxn2G/9zXo0pTuSkiQJe3t7/WdWJpPpW7ngs1OeVqtFqVQiiqKesGOTa1KkHZvk\nvyxEE0UxTiHal6T9I92dPKTRSDrF+EHSJkDn+RwZGYmNjU2cvueE5lepVAweMY+CVWYikyddCHTv\n7BQKV/wVB2ePZO3xS0SEvuPxtR1Ub5fyFKqNvStV2/zJrZNz2b3kV+p3XWEwOlOGB3Ht+BqqtVuf\n4jUTgiAIZMlXB6/cv/Dg4kr+GPnz/12qzFMUJWo0XDsyg9b9/2Tbkj4Efwgga/5q1Om8DotEXMpO\nbO5FtxHLkySYoPdv2Ll6ImEhn7BP74mXdw56j15t9P6KlqkFwLuAF1w9vYc9W9cSqQwhf8Fi1Gve\nCQdHZ94H+nPnxsVktT6lBFtWz6ZU1RY4u2SkftvhPL13iRG9m9F94ESy5SqQ6LUP71wmb/ZMeHl5\nmm0/OitYuVyOra1toq+NjrRjX6s709YRbOxCtNikrSNj3XGXjrABk0j7y++niIgIvLy8zPb3+K8i\nDQbSZsF3Q9IplQbVfdBFUcTR0TFRR5rY8w8cMgl7n25GEfS7l+exthbIWsD0StiEcHRDD8o3W2i2\n6nBBEChcaSDvXlxi/Yy61G4/H9dMOeOM2b3kV35uYL7CrcQgkyvIlLMab55dIlthX07tnkpUxDu0\nGhXuPsUoWLYdjulMu+ERNRr2LmuJMiKcvX+OonCFbrh7F07yurN7x1GlTjuc0xsu9NNoNPy9fQH3\nrp/GxT0HpWr1x80zN2um1GHAxOSl6N0yeVOreV8AoqPVPLx5hhWLphP8IYAXzx8wcf7Wr9rjGxjw\niscP7tJzzGflw+z5StJnwlbWLxyAt7c3rTr/ZvDa6Gg1Z//ZxO8LZpptPxqNBqVSiZWVVRy1P2OR\nUNGYRqMhMjIyHmnrvhdikzagLyY1lrQFQSA8PJzz588TGhqaonT3X3/9Rf/+/dFqtXTu3JmhQ4cm\ne660DK32v+lVKSRBWP+ZexNdCkulUultK41FbM9nGxubRD/ooigSEhJCunTpWLNuK7tOgUvmxC0P\nAaLVEdw83Je6XTebLRo8s3sEGbOWIUveWmaZ70uolMGc2z2Y7PnLU7xadwBObB+HjXMOshZqkipr\nfglRFDm0oinlGi+No3+u1UTx/vUVAp8dQxn2Bo1aiVvmguQp0YLIiCDevb5N6IdnhH96Q7RaiVxh\nhVxuiSCz5NN7P1wy+VC91WysbYzr7X378hbPLi+h05D4Vey3rxzhyO7lWFjaUbhsC3IVqaEvKNu1\ntAeVazUlX9FKZvl76LB52RisbJx49uASefIVomVn03vNk4PRfZry65AVOKU3XIF/7p8NXDm5g6GT\nl2L/Rd/0jrWz6dKmATlymKfoT9cSaWNjE6dn2pyITdoajUZ//qwjYZ0QSuw+bR1ik3bsjJSudczP\nz49BgwZx9epVPDw8qFOnDhUrVqRixYqkT29cMZ5WqyV37twcOXIET09PSpQowaZNm8ib17zdA0kg\n1e8SBUGQfvtDmfTAVMbMHrZIkmTW5/vdRNI6mBJJx/Z8TkiYJKH5Hz16zOZ9d/Eo0NeotW4eGUjF\npjPMRtCvHp1GG61ONYIGsLZ1pnLL5dw7t5Tti1pTonofPn14S74KX+9O/dyeoeQv0z2eQYlcYUVG\nn7Jk9IlpHdNqo/nof4M757djaeWIrbMPHrmLYefkiaWVg/7GS6NWcW53J2q3/91opTJRFLmwbyQD\nJsXtyz5/dBun/95AzkLVaNJjBTZ2cQvoHl4/QjpnB7MT9IvHtwkOek/HwZOQJInrZ3YzoldjGrXs\nTolyNcy6VmxsWTWL0lV9EyRogDI1WpOjYBkmD+tMg+YdKF0hRr3t+eM7ZHKxNgtB64o6NRoNdnZ2\nqerD/GWkLUlSHHEVrVYbh7R1589f9mnrIm3d94dCoSBPnjwcOHCAQYMGUapUKd6/f8+yZcsIDAyk\ne/fuRu3v0qVL5MiRAx8fHwB8fX3Zs2fP1ybprwKt+N+MpL8bkjY13a3zqrWwsMDJycmkNJlKpWLg\n8LlkLDDGqPGPrywmT7H6OLvlMHqNxKBWK7l6ZA6/dDCvYpUhCIJA/rLdeffyCjv+6ELV1r+n+po6\n+D89hwwZGbNVTnKsXG6BW5YSuGUpkei4Swf6UrXFNJOkRI9u7EWTjqOw/n+19fOH19m2Yjy5ilSn\n3dCdyA2orKnVKi4cmsvgaab1UScFURRZ//tweo+PuWEQBIGfyjeiUOk6HNo8k/3bV9Fz6EzcMxlX\noW8sAgNe8fTRA7qPHpHkWLdMWek3aQe7/hzP+ZN/02f4bI7tXcXi+Sn3y9bdWAuCgL29/VeX84yt\nXgafSTt2Fi92alyhUOjT3TrS1v2rI+3IyEjKlStH7ty5GTbMNB16f39/Mmf+/Fp7eXlx8eLX8XD/\n2vhROPadwJDnsykQBIGxE+bj4NPdqHPoD2+u8yngMq4eWTm/fzLKsLcowz4gajUxPtEyBYLMAlGr\nQRMdTobMhSlYvjMOzpkSnPPI2s6UqT/VbFG5MbhxYjHFa0zlzsllBHqepkjVAam6nkaj5sbRWVTy\nXWu2OZ/e2EKWXMVx9TA+ynhy8xAeHu7kKliGkKB3/DmvH04u3vgOWI+NAf9uHbYvbE/bPtPNrv61\nclZv6rcdrr9h0EFhYUm9tiMJDgpkzR+jsLKQ0WPoLJPf3wlh0dSBdBqywujxcoWCpp0n8uDGSQZ3\nqcuSRTNSLEOr1WqJiIjA0tLSYFHnt0BipK3T99eRtUwmIzo6Os55dVhYGKdOnUq24Uxa+Bt8LUhp\n0avSDPjuSDqxSDohz2dTsHb9dt5piuLqlHh16tvnZ3h6bQVhIW/JVbQZynABG+dSOHu6Ym3risIi\nfgWxKGr49PYmFw7MQRX+BgQJ73w1yFe6lV7Y49rReWTJWx1nt5zxrk8t3D23CifXgrh4FMfFoziv\n72/hr1WtqNJmBZaWptsSGoOTW3vwU7XRyBVWZpkvMvwjgc//plFP43Wt1aoIHpxfRr9JW1k9uw/h\n4RHUbDOD9G6JtztdPLySfEVK4eVj3pTjrUtHsLFzJleh8gmOcU7vTsfflvPs/mUmDGpLybJVqO+b\nMunXTStm8HNVXxzTZTD5WmeXTNStXYNCBQumaA/R0dFERkZibW1tthuP1IAh0tYVjOkU0e7cucP2\n7dspUqQIK1euZPbs2eTJkzw7WU9PT169eqX//1evXv1nK8X/q4Vj3w1JJ5buTszz2RQ8efKUTXtu\n41HQ8Dm0RqPiwbl5BAfewzF9IQTBhhI1JpIuUzGj5pfJFLh4FMPFI2Z8dFQYH16f4Z+1fYiOCkZu\nYYEoaanZPvVan75EyMcXvLh/nGK/LNT/zitvC5zci/P3ytYUrfEbXtnN6+T0+Np20mXIQ7qMibfz\nmILLB/tTq/1Ck27M/lnXmUzeuZk3pjVVmwwlSy7DvuCxERr0lue3DzFgknlMLnRQq1Ts37KAfpN2\nGjU+W94S9J28i3N/r2VkryZ0HTQZ72ymE0HA6+c8f/qY7i1HmXytqNVydt8CliyYYvK1OujaItVq\nNba2tmY1hfka0H0faTQa/f5dXWPsaGfMmIG/vz9Tp07l3LlzdOrUifz5TZN1LV68OI8fP8bPzw8P\nDw+2bNnCpk2pqzz3rZAWI2lBEDIDawE3Ygqxl0mStMCUOf5d72gz4EuS1qXIgCRbqxJDVFQUA4fN\nwT1//C+rjwG3eXxpIZIox8WrDtmKtib4/WWcrdRGE7QhWFg5kCl7LTJlr4Uoipzd2QbH9N4c3diN\n8k3nploUq4Moipzc2o+i1efFu6lxSJ+dEnWWcv/cFPzv/02puibJ1SYIVUQQT2/soGLzP80yH8C9\ncwspULoxjumNjzCObB1O0Ht/ipRtQo3Ws4y+qdu5pDM9Riw1exryjymdaNF9mkluW4IgULZme4qW\nb8T6+X3IX7AwDVv1MmndRVMH0W1k8o4cTu1fQp/ubZMd+SYkUPJvQewbDF2BmyRJ3Lt3j+vXr3Pk\nyBEyZszI5cuXOXnyJEql6dXLCoWCRYsW8csvv6DVaunUqdN/smgM0uyZdDQwQJKkG4Ig2ANXBUE4\nLEnSfWMn+G5asERR1Ju6h4SE4OzsjFqtTtTz2RT0HzyBt1I97Jyy6H/36Mpy3j0/hZ1TLtJ7NsTS\nOkaSU9SqeX5rLKXqL0cuN09q7vap8bhnqUh6z3KEfXzI4ysL8MhenGLVDfekmgOntvUng/cvuHgm\nHikHPj3EywfbqdJqGdZ2pus4x8Zfq1pQvOY07J3Nk7IL+ficx5fmUK+zcUIiHwOfcvDPHtja2tFp\n5E6TSPHI1gnkzJWTn6s2T+52DeLUX+sJ+hBILd/kv9aSJHFi7xIe3TrBkEkrjCLO1QvHkjlnKX4q\n39Dk9d6+eoz/jc2MHDYwWYYUsQVKkmqLTIvQ1b7o2kFlMhmiKLJ48WLOnTvHunXrcHQ03dozjeKr\ntGB1nfoxtZdJEsuGuyTagiUIwm5goSn63d9NJP1lujs8PBxRFI1urUoM23bs43lQVlx9Ygj63cuL\nPDg/H1fPmmQrOjmeTvfLu9MpUH642Qg66M0N0GpI71kOAAeX3BStsYh3y9tT1QAAIABJREFUfv+w\n5/eGFKrUk6z5zNt68/z2QQSZfZIEDeCevRYOGQpzZH1X8pfrRNb8yWsLu3p4OlkLNjIbQYuiyPXD\nw2nQLelIUK1S8vf6PkiSBXKZQKsBq00i6IBX91F+8uPnqiNTsuV4CAsJ4sLxXfSZuCNF8wiCQOUG\nPchRsBxj+jXn1z5jyZUvYd1tvyf3+PAhiAa/mk7Qoihyeu885k0frc9ixa52Toq0UypQ8q1hqAI9\nOjqawYMHY2try44dO/51afu0gLR+Ji0Igg9QFDCpvP7flR8yA6Kjo4GY/kZHR8cUfxhevnzJqo3n\ncPWpjVoVwsW93Xh19wDZikwgXaYq8Qj6Y8AxXDzy4+iavEKQLyGKIg8uziFnqbhiFYIg4J71F36q\n8Tv+Dy9xcHkLQj48N8uaKmUwt8+sImdJ4yu4bR09KFFnKa8fnOH45p5oNGqT1nzvf4ewjy/xzm8+\nkZTrh0dTumZfbO0Tj+7P7pvG7iXtyV2yO1bWDlRrMgAHJ+OLpERR5K81A2nbd1ZKtxwPS6d2pXWf\neWZL9WbOVpDeE3awZ8tqNq00bHAhiiJL54ykZa/kKYOdPrCUPt3a4OzsjKOjI/b29igUCv3RU1hY\nGEqlkqioKL0IiA66iuiEZHnTOnTPMbZEaUhICL6+vhQuXJh58+b9IOhkQhKlb/6TEP6f6t4O9JMk\nKdyU5/XdvBskSSIiIkJP0uZIkWk0Gvr9NgO3fMO4f34+H1/fxDN3N6ztDFd2a9ThhL4/Tsm6y1K0\nbmzcOj6CXCV6GawGB5DJLclapDsq5QcuHZyO3EJGhSZzUFhaJ3vNoxu6UrDieGQy094+MpmCPD8P\nIfjdLf5e1YZM2UrxU7VBSV4niiKXDoymQrNVyd1yPAQ8P4etnSVZ8yecYXh0fT9Xjy0lV7G2VGrZ\nh8AXV7Cx0ZCvRD2T1tq3qh8NWw/Ezt48bmA6HNy6kEI/18Y1o3nNM6ysbekweCln/17L+AEtGTp5\nJda2n+sbls4eRq3m/bG1Mz0dG+j/FAdZEMV++hylJ2RyEdsDWndeK4riv7JADD5nAGJXoPv5+dGp\nUydGjx5N7dq1v/EO/934FpH0W7+zvPU7l+gYQRAsgB3AekmSdpu6xncTSeuEARwdHZHJZGaxNRs9\nfjYh2vyc29kJJFey/zQhQYIGeHlvBgUrjjabpvW7V+ewtHLA2T3p4jNrW1fylZ9Ephy+HFzZlkdX\ntyVrzSt/TcErZz3snJKfcnZ2K0SJOsuwsPZi/9ImPLmxJ9Hxp7b2onDlIVhYmceuT6NW8ejSQio0\nnmTw8Y8Bj9k6rzH+z25RueU6suSri1YbzcPzs6nbwbTo8cnd09hZy8lf3Dy+4Dp8CHzNozsXqVC7\nk1nnjY2yv7SjcdfpjB/chtvXzgLw4PZlotQiBUpUN3k+URQ5s2ceQwb2TnScjrRtbW1xcHDA1tZW\nL/IBoFQqUSqVqNXqeJF2WoWu/kXXPQJw8eJF2rdvz9KlS38QtBnwLSJn9yxlKFxhsP7nSwgxkeBK\n4J4kSfOS87y+m8IxQH9XHhwcrE+xJRd79h2iZ++RZPAojXu29sgViUem71/uwyG9Dd4F2iV7zdjQ\naNRc2teZYjX/MLlXWJJE/G4uIVr1lootFhmdKn3/+hY3jv9B4SrTkrNlgxBFDS9ur+HD63MUqzkK\n98xF4jz+9OYeggLuULCC+bSnz+3qSoWGI8jgFbeF633AQ87snoDC0onClYdjY++if+zsjm7UajUU\nTxP8kTVqNetnNmTw1G1YWiU/c2EI0wY3pNPQlcnqTTYV0eootiz5DWdHWx7du0nfSduxsja9c+DU\nviU0/aUQJYobb6/7pUAJxNfLBuLIbianEC21EFui1NbWVp8R2LFjBytXrmTz5s1kypSwMNF/BF+l\ncKz1CP/UXiZJbJjiGadwTBCEcsAp4Baf+XS4JEl/GTvnvy9nlALoisZS+gH+8OEDI0YvIlfxidjY\nGxdRRoRcJn/55SlaNzZuHRtKntKDkiXmIQgyshbpSfDbK+xb0ohKLRbg5JJ4ylTUaDi3ZzQlai9J\n7pYNQiZTkLVwJ7zyNOfhhYXcPDabco1nY+vghioiiEdXNlKxhfmsFp9c30SWXCX1BC2KIleP/cGz\n20dI55abItXGY+8U1zXr6c1tZM9bxCSCBtixpDMtu08AQUag/3M+vHvFpw8BBH8MJDTkAxGhwSjD\nQ9BooilaujoVarU16sZx24oJlKvZ9qsQNICFpRVt+i5g1tAGRCpVREepTCbpt68e4yAPMomgExIo\n0Vk6Wlpa6lPgOtLWmVPoSDu2ycXXRuwWsdgV3LNmzeLu3bscOnQIW9vUbZP8npAW+6QlSTpDCjPW\n3xVJ65BST+k+/SfimXcECkvj0q9BARdwy1LGbF8Ub/1OYefohaOracIGX8I5Y3EKVZrNmZ0jyFbw\nF/KWTjjKP76lB3nLDEKRSr3XFlYO5C07goiQ15zdNQJLG1uUoW8pXmua2Y4HlKGBvH9xhEY9N/Pp\n3XNO7x5PtFqNT4GGVPJdg8yAxnZk+AfePTtIh2HGaWxrNBrOHfqDy8c3YOeQnv3bViFXWGFnnx5b\nR1ds7F2wcSlEuizO2Ng5Y2PrhCCT8/TWYRZP6U1E6HsyenhTq1kPMmWOrxr36vl93ge+on6HcSn9\nc5iEu1eO4e6Vl59r92bxpM5UqduWEhUbGXWtqNVyZu88li6catR4UwRKBEEwSNqxTS4gLml/jX5q\nXQW3TCbTF4hFRUXRt29fvLy82Lx5c6oaf3yPEP9vVvJfw3eV7tb1SYeFhenbN0zF0uXr2HxAg42T\n8RHBsxujKFF7kdkI7tK+zhSuOg+5hXlSqJIk8fL2SpRhT6jiuwTZF1+KD69uJcj/CdmLmSZ0kRJc\nPTyMyLBArK0tsbRxJnO+hnjlrJyiL9gTm1uROVc5/J+cxylDDnIW74Rj+iyJXnNyc2t8+yzB2TXx\njMmD60c4d3AJyK3Jmr8Oj66so8OIPQbNNRKDJEkEvLjNvYs7+Pj2MYKkoUSFupSt7otMJmPa4Ab0\nGLMRWzMXoSUGjVrN7OGN6TB8FwoLS0StlqPbJhIe/IouQ5cm+Zoc372Qtg1KUbhwoSTXih192tra\npphQY5O2LtqG1CVtQxriHz9+pEOHDrRu3ZqOHTummXT8V8JXSXc3H+SX2sskia2zfX5YVZoDyY2k\nX758yaYdN7B1N/5cOSryI/bOnmYj6IhQf2ydMpuNoCHm7+FdqDMh726wd2ljKjSdRXr3XAAoQ9/x\n+OpOStT+w2zrJYVP7+4jSBpK1o7xZo4I9efTmzO8uLUDTXTY/0m7AV45qxj8ghU1Gj69f8SnwPuE\nfnhMZNgb3r+5g71zRqxsPano+ydyI8xPbp+cTckqvgkS9IeA5xzeOomIsBAyZv2Zck0XYm3rzPFN\n3anVZpLJBA0xr4WHTyE8fGIILTIihEfXD7FoUi9ePbtJoVLVvypBA6yY3pnabSfr+8JlcjnVfcfx\n/P5ppg2qR/v+c/D0zm3w2jd+98lgG2kUQccWKNFFnylF7EgbSPVIW5eij+1h/ejRI7p168bUqVOp\nUsW8BYQ/8BliGu+TTi6+y0ha90VgbW080YmiSONmvYi07pBkkVhs+N2eTr6y/XBIny05W46Ha/8M\nJPtPfbBzMq/VoA7RUaHcOzOezLnLULB8N/YvbULBSlOxsXdPlfW+hChqOL+7I0WrLUBhaWdwjDLU\nn08BZwl5d4NodRggIVdYIhMsEGQWCHJrbOzdsbLzwtLWgyjVJ5QfT1Om4Vyj9/Ep8DEvbiymZf+4\nSmQatZoj26fy8sl1nF1zkLt0R9Jl+Pzavnp8ik8vj1OzjXGpXWPx9uU9zuyfRwaPXLx8eIa2/Wbj\n7ply7+WkcOXkLp49vkfVZoa1uSMjQti9vA858xamtm/cvnmtRsPuZf1Ztmhakmft30qg5EvS1llE\nxvaANoa0JUnSm2TETtGfOnWKsWPHsmbNmmSbZHyJX3/9lQMHDuDm5sbt27cBCAoKokWLFrx48QIf\nHx+2bt2Ks7NzEjN9NXyVSLpJ36epvUyS2LEgu9kj6e+SpHVqPzY2hnuLDWHq9EX8cyEDNo7Gf9BE\nUcT/4RSK1zKPx7Ioilz7uy9FqiWrkt9oSJLE63vr8Lu/h7wlupApp2l9wSnBtX8GkCVvKxwzFDbL\nfKKo4ebRnlRtvQYLK8OkH/8akVObW9Jh2BZs7Jz0vzu8dSp+D69SsHxXPHNUiEckoijy16qmdBi2\nC4WFedy5dFg1uS5Ne63Hxs6JiNAPHNs+BrkQTYcBi7A04WbTFKiU4Swc15oOw3YhS+T8VJIkLh9Z\nzqPrf9Nz7Bqs/19UdmT7HLr4ViZfvsS1oqOiooiKiooTfX4rJIe0Y1dw6wrEJEliw4YNbN26lc2b\nN+tNM8yB06dPY29vT7t27fQkPWTIEFxdXRkyZAjTp0/n06dPTJtmvi6MFOKrkHTDXo9Se5kksXtx\nrh/p7pQgMSesxHDnzn3+Ov4GO/eELQANIdBvO165Gph0TWJ4cm0ZHrnqm22+hCAIAo5uJZE9Osmj\naxuwdsxKOnfzOU4lhFcP9mHrkMVsBA1w78xIiv8y0miCBrj69wiqNR2sJ+irpzZz6fA68pfpSM2O\nAxKM8s7sHEi1ZiPMTtBHtk6gWKUO+v3YObpS79ffCfC7ztxRvhQuVZmazfqZdU2AZVN/pV7H2YkS\nNMS8X0pW74pPvkrMGdGCeq0G4JzOFa/0JErQX5JbWiikip0et7KyikPa0dHRqFQqBEHQt3vJ5XJ9\nylwn8anVapk4cSIBAQEcOHBA3zpmLpQvXx4/P784v9u7dy8nT54EoH379lSqVCktkfRXwX813f3d\niJnEhikkHR0dzW/D52KTwXQ5SlXYLdyyVjP5uoQQHHCFDJkrmW2+hCCKIvfOTCFb4ZFkKzKRBxeW\n8vDSolRdU6UMwv/RHrIW6WG2Od88PUgGz9y4ehrfOvXm2VmcnGzIWbgafo8us2RsXQL931Kr02Z8\nCtRJkKDfvryOra01PnnKmWv7AAR/eM2HN0/IVzL++y+TT1FaDdqJKHNh+qC6PLh11mzrnjy4Cu88\n5cjgYbwvuZtnLjoM28WF4/vZ++dY+vdJ2Kdad+wkiiL29vZpgqANQUfaVlZW2NnZ6cVVZDIZ0dHR\nhIeHo9FoePHiBVu3buX58+d07NgRBwcH1qxZY3aCTgiBgYG4u8ccSbm7uxMYGPhV1k1LEEXxm/+k\nBr5LkgaMJulRY2ehsqxnsgRm6Md7pM9UyGztQ+/9r5IuY5F4WuCpgftnJ+GetRkKCzvkChu8CwxF\nE2XJ+d2d0KhNt8szBtcPDyJvmbFme35qVTAfXx2iYIWBRl+j0ah5cmkR5er0ZdWUplw+tp1qbVZT\noFw3g+1ZOoiiyLV/JvFL68nm2Hoc7F7emxqtDWtoQwyJFCrbmmZ9t3DxxCHmj2pOaPCHFK0ZGvyB\nq6cPUbaOYV/0xKCwsMTVzZ25MyckSLxarZbw8HAUCoXZCsS+FmJH2lqtFisrK+zt7QkNDWXjxo2U\nKlWKCxcuEBAQwI4dOwgKCvome/w3/U3NBVGr/eY/qYHvNt1tDPz9/Tl/NRT7jIm36RjCx9dbKFoj\n4S9XU+F3Yxn5K0wx23wJ4VPgHaKUEbj5lIzz+3QetbFxLMDZXZ3I+/MA3LKUTGAG03H/3HQy525k\n1uK0+2dHUKbhLAQTKnXP7+6JKAnsXzeBUvWm4+DskfRFwIX9o6lQry9W1san1I3az19/kLdYHRyc\nk/67WFrZUrX5RD69f8HqOQPInDUnjTuOSda6y6d1pkGXRcn6on/95DKFs9uRO5fhCDwhgZJ/E9Rq\nNSqVKs4ZuoODA8HBwRw8eBA7OztOnDjBmjVrsLS0pEED8x15JQR3d3fevn1LxowZCQgIwM3NLdXX\nTGtIi2ImgiCsAuoA7yRJKpicOb7LSNrYdPec+auxSme6raJGHYG1nTNWNumSs714UKtCsLR2wtI6\ndVtvRFHk/rkZZMrV3eDj1vZZyF50Mn63tnL3tHmql4MCbhKlDMbNp6ZZ5gN4dv13cv7U1GhLS1EU\nOb6lF8rwEErWHkNl38VGE7RKGYyoDiJXkV9SsuV4UIYH8/jWUYpWMk2bO10Gb5r0XIutUw5mD2uE\nSmmS4Q7/bFtI3mJ1SOdqevdAtFrFs8t/0qv7r/Ee050/R0ZGxtGv/jdB9xxUKhV2dnZ6gj58+DD9\n+vVj8+bNVKhQgWLFijFo0CD279//VQgaoH79+qxZE6PMt2bNGho2NN1C9N8OrVb7zX8MYDWQoi+3\nHySdANRqNTfvvsfCynRifPNkJT4F2yZ3e/Hw4MJsvPK2Mdt8CeHemfF4ZG+FQpFwT7dMbolX3v7I\nFZk5u6MdalVIstcTRQ33z88iV6lhyZ7jS4S8f4CoeUfWQk2NGv/01h4OLG2IMtSfhj13ksEz6X7e\n2Lh0aDzl6hlv2Wksdi7pyi+tZyQ7bVmgTEuq+c5k7ihf7lw5ZtQ1wR/fcu/WOUpW75KsNS/sn864\n4X0MVj8rlUo0Gk2KNfO/FSRJIjIyUv8cdBrcK1asYOnSpRw4cIDs2VO/JQ6gZcuWlClThocPH5I5\nc2ZWr17NsGHDOHz4MLly5eLYsWMMG2a+z9S/Bd/aptJQJC9J0mngU0qe17/v05ICmFLdvW7DdjQW\nZUnO/b4kBuHsHv/LXpJE1KoQopRBaDUqnDLkNuqsOyriHU4Z8iVjJ8bjY8BNNFHR2KUzrsjK0a0S\nVg55ubC3FzmKdcQje1WT17x+eDC5Sw5I0GbTVIiiyLPrs6nS+s8kx34MuMflg+Nwdi+OtV06KjQe\nm6z6gejID3rhEXPh9oVdeGYrRnq3rCmaxyVjdloO2MHhzcO5c/kffHskXu27ckY3GndflqwbA797\np/m5UEa8veMeDaWGQMnXRmyJTzs7OwRBQKPRMHLkSKKiotizZ89XbR3btGmTwd8fOXLkq+0hLULU\n/DdlQb8rktbBGJLee+ACtk6mpRolUUvAs02oIz/w4cE8rCzA0lKGlYWApQVYWcpwdU2HZ94MWFtb\ncubcMd5+UBNFJuzdKxi0f3xxdwduPpVN2oepEEWRhxdmk63IRJOus7JxJ1vRSbx9upaXdzZTqMpE\nbB0yGnXt6wf7sHfKiqOr+Vq7Hp4by0/Vf8PS2iHBMSplMGd3DUQmdyJ36cl8CryGp7OM9BlNF5q4\nf3kz+UrUScmWDeLaiTW06LfVLHMpLCyp1XY2Dy7vYuZv9ekx+k/sHdPHG7d/4wwKlWmGY3rjXr/Y\niIoM5+WNTQyYPkpfEKYrGouMjPzqAiXmhCGJz7CwMLp06ULFihUZMGDAV9EC/4GkIUn/zRasHyRt\nAFeuXOOTMgv2RtYBqZSBaEOP4pEhigHj6lOxwiSjUnq+zWMMCl68eMHOPf9w8+5WgkIEBPsipMtU\nGoWFDW+fHaRo9YXGbSSZuHd6PB7Z25ikpKaDTKYgY/ZfiYp8z+3jk7GwtqZQlYkoEplLpfzEq4d7\n+KmG+dq6Al+cxMk1E25ZSht8XBRFLh8aQ/C7l2Qt3BtbR29EjZqPr3ZSv3vyvLVf3NlFxd/MQ6Y6\nvPd/TAaPPMgV5o3M8pRoRMasxVg8oSM1GnelaJnPNxfv377k+cPbtBo4NFlzX9g/janjBuHk5KTX\nx46MjESSJL2wh1arRS6X/6uI2lCRm7+/Px06dGDQoEE0atToX/V8/uvQfoNIOvj9NYLfX0vVNb4r\nkjY23b1oyWZs0zdPdC5J1BLx6RK2wh1KFfKkV48+yfaF9fb2ZkDfmHPA6OhoLly8xN4Da3n5MhRB\nkCGY2P5lCkRRQ2T4e9yzpUxAxMomA5nzD0UZ+ogLu7vj6lWMPKX7GBx748gg8pUZbbZ2K41aScCT\nzVRru97g4w+vbOTp9Z1kydsOz9yf9/T46gTKNhiXaHtVQgj5+AJ3jxypIFwyjuotp5t1Th2cXbPg\nO2A7x7aO5s7lw7TtF6Nc9+fsXjTv82ey5nxy6zDVy+bWv/flcjnR0dEIgoCtra2eoFUqlZ6oY3s/\np1WS06mgxZb4vH79Ov3792fJkiUUK1bsG+/wB77Et6judnIpipPL5yPCF/dXmX2N74qkv4Qhb+kP\nHz7g9xps3Q1HMlGR79GEHsHTTU2PrlWpUMFXLwVoDlhYWFC+XFnKlysLwPkLl5k5bxqSU02c3Ix3\n3jIWT64tI32mGmabz9YxF1mLTCTswxlOb2uDT6GWZM79OWp7eHE+HtlrY+PgabY1754ZRuk6k+OY\nZmjUKq4fn8VH/zu4eJSjYKWFcW4KPry5QAYPHzJ4Je/m5Mpfk6jTblKK9x4bMQ5NAk4u5vvbfAm5\nXEH1llN5fPMQ0wfVJXPWPBSv3A57J9NlKyMjQgh6cpBWvWP+DrEld3XqW4D+vFaSJL3cZmRkJKIo\nxjO2+NakHVsFzd7eXp8J2L9/PwsXLmTXrl14eRnXNfADXxdp0apSEIRNQEXARRCEV8CY/7V35nFR\nluv/f88Mwy6KCxgoUu6oqAm55E6upcdjubQcRSU8aQtl33Dfzd0ysqxMU1yi7GTmgmkuZUqpJ8lc\nUlQUDYQCZGfW3x/+Zs6gLLPPAPf79fJVIs/zXDM8w+e5r/u6PpdWq91UxWFlqJUirftFcL9Iq9Vq\nVq/5GFmdAQ8cU1KUjqxoLz3Cgpj84st4eXmV2aeyFd27hfPVjjA2fvY5X+9biWfgC3jWMW/FXh7Z\nf57hkU7GzQU2FolEgk+jXng36E72ra+5+XsCIT3fQiJ1pTD3Jg93tJ6r2I0LOwhq3Zu6jVoA8Oe1\nE5w//gESiQeNHxlBu15R5Xhsq8i6vo1hk81LVWs0GqRSFfX9mlkcvyE/7l5Fx162r+IHaNlxCG6e\nDfnygxcZGhRu1jl+2buMlfNj9FaY9+/d3o9EIkEul+tFW6PR6NPjuvGU93tk21O0dVXo8D+LT41G\nQ1xcHD///DP79++nTp2K6x0EjuX47t6ODuEBtFrts5aeo1aJtOEH/v4Pf2lpKfn5+ZxJvo1bw/+t\n/NTqUkr+2kXXTt7MnrlEbwdY1TB6a8c9acKzjBk1jCXLP+C3yyrqP/yCxeMq/7p9Gu96ITZzMZNK\nXWgYNIp6Dw0l5cxn3Ek7SXD70agUBbi4elt8/qL8dAr+PkWnfh/wy/6FZKdfwKdhKM27zMW1kta5\nlDNL6P7UTGQu5vXqnj36Po/2fs7csCvk5uWf6fHk/1n9vBVx5KtFPPPqt1xM+owLp8fz3OubjM4I\nXfl1P0/2D6VRo0ZmG5RIpVKkUmkZ0dattBUKBVqtVp8Wt7Vo66rQXVxccHd3RyKRoFAoePPNN6lT\npw47d+6slq1jtQVrD7VwJmrdXafbj9b9V6vVUlhYiEql4vCRnyiRhePN/3+qzv4JvzqXiHvvVYKD\nm+lTeXXq1HFIWs7b25uli94iNTWVuYve529VO+o3HWx2LNfOfkyTNm9ZOcoHcZF7oVYpaNYmCq1S\nw7kji1Gr85BIJdRv2oemrYdXWmhWEb8eegU3D19+SIjhoeYjeahFdJXvxd2sC/g2bIB/M/Md07Ju\n/MTQZ980+/jySP3jZ5o2D7dbpfDJxHU80v5JvHz8CRsYy53Un/lwzhBGRq/hoWbtKj22qCCXu6kH\neea1RZSUlKBQKKzy0CqVSnF1ddULvaFol5aWAtab+2xIeWMyc3NzmThxIsOGDWPKlCkOT8MLai+1\nTqR1SCQS/VQbuVxO3bp1Sdh5GK96EygpvImsaC8x0cMY9tRkFAoFhYWFuLu7I5fLHf6BDQ4OZsun\nKzh0+Afi1r+NS8N/UqeBaX3UipI8XGR1kLvaPn2Xl30JNGp8GtyrvPZp2AMAlTKfortn+e37OWhU\n+Uhd5NRv2o+AR/qTn32Nu9kplObfRFF0h9LiHKRSGRKJCyAj5+8rBDwSQXD7CcjdfIyOJf3KRgaO\nM390aMbNXwlq2cXqYnr829UMm/ihVc9ZESVFeVxOPszQSdv1X/MP7sqgyHgSP3+ToBbtiXi64oe3\nX/YuZfXCGH2KWrd3a20MRVs3jUqXHtdNozJ17vP96LIAhhaf169fZ9KkScyfP5/Bg63nhGfI0qVL\n2bp1K1KplA4dOrBp0ya7DeMQVC9q1TxpuOckptFoyM3NBdDvLf/xxx9MmLoFV5dSendrzPS3piCX\ny/WtJB4eHk45qUetVrNu/WckHrtFwxZRSGXGte6cOzaPOg2ewKtuK5vGp9FouHLqTZqFzEHmUrlp\niVJxl6LcXykpuoqrW0Okcj9k8oa4utVH7lYPieTe+19SmE7eXzsJ6Wmal7lKWUT65Xd44vn1Zr+e\n77b8i2de+hBvH+vNB1aUFLFrwyv8c/IGq52zMravGUPXoQuo2+iRcv/90s+buXEhkRemxePuWXZb\n4tKZbwlrVsjggf2QyWR4eHg45KG1ornPhpXjlYm2VqultLQUhUJRZkxmUlIS06dP59NPP6VDB7Os\nlqskNTWV/v37c/HiRdzc3BgzZgxDhw5l/PjxNrmeEyDSEBZQ61bSGo2G/Px8AP3Ts1qtZtWaD3mo\nfjHvrJpFYGCgfgydPYrDLEEmk/Hq1EkMHnCFN2ctwz1wIp5GVE4X56XT+BHbCjTArYvv4d9sVJUC\nDSB3rUtdv77UpW+l35d58yPa9za9TenGufV07jfB5ON0KBRFeHp6W1WgAb5LmE9YhHlWnKZy4Zdd\n1H+ofYUCDdCm63gaP/w4G98eQ8Qzb9C60z03ucL8bApuHmZQVKx+heuoz0Vlc58VCgUqlQqpVFom\nPW5YMKqrLjes4P7yyy/57LPP2L17N40bm27qYiw+Pj7I5XKKioqQyWQUFRURGGi7in5B9abWWeXo\nhFe3f6abA7p0yWy+2PEBAQEBFBcX6wcB6IpInJ1WrVryRfxKGkt0m1wCAAAgAElEQVS/Iff295V+\n782LX1PXr4fNY8rPuQwaFV51jZ/nXBVZadtp2noEru71TD5Wo/qTxsHm70WfObCMrmb6WldGzp1r\nNG3R1ernvR+VSkXSwQ08GjGtyu+t59eCoVE7OPvTXv7z0WsAJO1ewluvR+Ph4eF0D673z3328fHR\nr/JLS0vJy8ujoKCA4uJiCgoK0Gg0+tZJjUbD8uXLSUxMZP/+/TYVaID69eszbdo0goKCCAgIoF69\nejzxhPXmzgtqFrVuJe3j41OmX1NXYerr64tardZ79Npqn82WuLu7s3b1POK37mT7rjj8Wk9GKnuw\n2jY9ZQ/BoQtsGotGo+HPP9bTrN0cq52zpOgOatUdGjWrWmTu507qEZq17We2sGTfSSHtj8P4N/Tg\nz0sHkEq1yKQgk4JUCjKJVv//Eq2GvCI1apcGBLUbTOOg9hVe9/ypb3mkvW1tX3Xs3vASXYfOMtq8\nRebiSo9/vM3Ni9/xXmw/Yt+YSJMmTZxy2+d+DFPfcG/1rNt/1rWMPfPMM4SEhHDp0iXat2/P9u3b\n7fKZv3r1Ku+++y6pqanUrVuXUaNGsW3bNp5//nmbX1tQ/ah1Iq0zx3dxcaG0tJSCggK985FKpdK3\nkTjTKsFYdH2e/xwxmO7dOvF/s5YjfygSL5//jR3Mz7mOu2cTpFLbDgS4l+Z+xqg0t7Fk3viQdr3M\nG5GZfXs33YduMemYovwsbp3/Dy7Km4R3as7MAzvx8/Mz6t7QarWkp6ezZ99Bftu3lYJSOQ2bdePh\n9hG4uv3vPTlzeBNPT403+fWYys2U00hkXvgHme6U5d+sK507tWfMqJHV8nMB6F3PPDw8cHV1Ra1W\n88ILLxAfH09KSgrHjh3j9OnTDBs2jJiYGJvGcvr0aXr06EGDBg0AGDlyJCdOnBAiLSiXWifSixcv\nJjQ0lJ49e+Lt7U1mZibXrl2jXbt2SKVSvduQi4sLcrm82qymdW0kcrkcT09PWrZsyRdbVxM7aznX\nbgXj2+TevOMrv7xLo+Aom8aSn3MZrVqJVz3rOaT9lbaTwBZDcfN4cDhEVZQUZeHrF4TcteIRnDqU\nimJuXdyDIucsbR5uyNK3RhIUFFTlcYboHpZ8fHyImvgvpFIpKpWKn38+xd4Dy8nMKcHFO4hGwV3x\n8Q3A1a3quCzlyM5FDBj3mVnHXjnxDnHL3qi2Aq1QKCgpKSnTJpaSksLatWtZvnw5/fr1Iy8vjx9/\n/JE///zT5vG0adOGRYsW6XvLDx06xGOPmb8NI6jZ1DqRfuKJJzh48CBxcXHk5uaSnp7O6NGjCQ8P\nx8XF5YHeTMO0mWHxibOg1WpRKBSUlpaWaSMBcHV15Z2Vc/hy57ds+nwt9Zu/iFqlxt3Tz6YxZVz5\nhKZtZ1jtfIqSv1Eqr+P38MtmHX/z93X0GF5xS5FGoyY95Qfybh0hoJErrz47lM6dnzbrZ63bMjE0\nxYB7/b2PP96dxx/vDkBaWhqbtyYglxTxd/oVGjzU0qzXZgy3rv2XRk064epm5MQYA+5cT+KJno/g\n7+9vg8hsi6HFp2EF97Fjx5g/fz7x8fG0bt0auLcN9uST1p9oVh4dO3Zk3LhxhIWFIZVKefTRR4mO\njrbLtQXVj1rXggX33MVmzJhBQkIC0dHR3L59m+TkZJo2bUpERAT9+/fX+/MairZKpXKqAQEajUbf\nIubp6Vnpqv/GjRuMee4l8OxHg0Db9H4C5GadpTg3mYZNxljtnDcvLiDk8YW4e5n+cKHRaLj+6yyG\nTnpw+IZareTamc14aq7zz6f6MOCJfhYZcpjjvFVaWso7733CpZulhPZ/FXcP6/etb18zhp4j1+BZ\np5FJx6lVClKOTWfrpyud7uG0KnTZDMPPhlarJT4+nq+++orPP/9cn24W2JzqdfM4GbVuJQ2QnJxM\nWloav/32m/6DqtVqSUlJ4bvvviM2NpaMjAzCwsLo378/PXv2xMvr3ipErVbrfxk7ckCALr1tbItY\ns2bN+OHILmbMXsGvlw7jUb+/TeL66+YXBLZ83Wrny836hUZNupol0AB/XtlJq0fLepNrtVpu/r4L\nTc5Jpr86jvbtTZsbfj+GPbemOm+5ubkx/f9eJj09ncXLF0LdToR0e85q95FCUYJE5m6yQANcSfqQ\nebGTq51A6yw+ZTIZnp6e+kKxhQsXkpmZyZ49e4RxiKDaUCtX0sagVCpJSkri4MGD/PDDD0ilUvr0\n6UNERAQdO3ZEJpM9sMqGexN/bJkaNxSE+9PbxrJrdyJx6xOR13/erBnSFaFU5HH70jqrivTNiwsJ\n7bcKF7npqVqASydiGDY5QV/RnHH9J3Ku/ofoccPp399yQ35TshnG8OPxk3y06T8Eh40n4OEwi+P7\n7vO5+D/ch8AWvUw6LifzCr7F3zJ3pm2LqKxNeYM+ioqKmDx5Mo8++igzZsyoNnUmNYjq9ZTnZAiR\nNgKtVktubi6HDh3i4MGDDkuN60YBAhYLQnp6OlNeWUQeg3D3rtjYwhRu/L6aen6D8KzTwirnU5Tk\nUJD9Fa26mtfGlZedgrroGN2emk92xiXSz21i+KAwnhs70iq/qHWCIJfLrdpPr1ar+WTjNo6fvk5o\n/9fxrmt+DcGWFSMZMnGHSbFptVrOHXiDbRverlYrzvIsPjMyMoiMjGTq1KmMHj262mUFagjiTbcA\nIdJmYJgaP3jwYKWpcZVKhVKptDg1rvsFZE0HNLVazbwFa/jpvxo8Ggyx+JxXz8wkKGSuxXHpuHX5\nXVp0ica7XnOzjr90MpZuT77FXym76NbxIV5+KdKkKU2VoasYNjebYQw5OTksXfUhOQo/QvtMRuZi\n2nWunDvMjT/O0KnfayYdd/W/W3lukD/duoY53bzn8jAsnjTcbvj999+ZOnUqa9eupUcP25v3CCrE\n+W6aaoQQaStgbmpc1+ZVmc+wrkLVluMxDx46xvI1O5H5Pm92Wjkr7QCoS6jnP8gqMWk0Gu5cX0mH\nvu+adbxSUcCpvaN57vkXiJ02mbp1Kx5daQqGFcOenp52MfY4f/4CS9d8Suuer9HgIeOtXLetepq+\nYz/CzcP4ASRF+VkUX13H2pVzK7xnrT2FyhJ0Fp9qtVrvIAZw4MABVq5cybZt23j44YcdHGWtR4i0\nBQiRtjLWTI3r0tsSiQQPDw+b/lLMyspiyqsLyVb0xr1OG5OPTzkdS9M2s8p1ODMrntt7adA4AL/g\noSYdp9Woybn1DQ/Vvc3L/x5NixYtrLYaNPx56AqS7IVSqWTh0nfJ1bakbdexVX5/UUEu+7a8Rd8x\n75t0nQvHlrNu6cRyK5/vv2etMYXKEnRjZg1/Hlqtlo8//phDhw6xbds26tUz3T5WYHWESFuAEGkb\nY2pqXDfRRyaToVar9elte/wC1Gg0LF2xjkM/3sWj4TAkEuOuWVxwm79vfoX/w9br9bx1aSGhEXFI\npcZnDu7eOY6nOonp0yLp0qUT8KCwgHmrQVOr6W3F3n3fsWN3EmFDZldqgvLtxtdo/ugL+DXtaPS5\n1SolWb8u5IN3q7aMvX8KVWUDLWxBef3oKpWK6dOno9Vqee+992y2DSEwGSHSFiBE2s5UlRovLS1l\n8+bNPPfcc7i4uKBWqwH7phmTfj7NkuUbKdD2wLNu1b/kr51dgF9QJG4e1jG8KMq/gar0JI90Nq5K\nvCDnD7S5u4l8YQAjRzxZoTiYIyyVmcU4itu3/2T6vNW06D6VRoHlzxGPXzWKIRO2mXTe6799xb9H\nNqVrV9OryrVabbkPmrbwFNA9MLm5uekL2/Ly8oiKiiIiIoKYmBin3DuvxYgfhgUIkXYg96fGk5KS\nyMnJISQkhOXLl9Oy5T0XKkcYqmi1WjZv+YIdO4+jch+Ku1eTcr9Po1GRenaRVR3Gbv2xjDbdZ1XZ\nG11SmEnJnc8Z0KclL0+JNFlAqxIWnU2sWq222/6zsahUKpYsf4/M0ia06zGuzL+dO/klOX9nE9Ld\ntLGcl4/MIP6TxVa5n3RDbHTvr1qtLnPPmnvfllewd+vWLSIjI3nrrbf4xz/+YZPPQ25uLlFRUZw/\nfx6JRMLGjRvp1q2b1a9TQxEibQFCpJ2EzZs38+abbxITE0PdunU5dOiQ0alxW1bglpSUsGzFB/yQ\nlI5LvX8idy3riHX7SjwensHUqR9uletpNAqybn5Au14Vz4tWKYvIu5VAaCsXZk2fYtWiMMOHIY1G\ng0Qiwc3NzWmrmw8cPMzmL44SPnQubh7eAGxZMYKB47bgIje+Bz474xItvU4w9d+RNonz/vdWq9U+\n8EBU2Xtr6A9gaPF55swZ3njjDT766CMefdR6XvH3M378ePr06cPEiRNRqVQUFhZa7b6rBTjXh6aa\nIUTaCVCpVEyYMIHY2Fjat2+v/7olVePWTo1nZmYyZ/5a/rjhgUeDJ/V7xSmnYwkKmWf0/nVV3End\nSkDLXvg2fnCVUlyQQXHWPgIblTBv5r9NHnxhLIbtbrrhGM5a3Qz3eoFj56wiOPxF3L0bcfirZfQa\nucqkc1w4sohP18boHwRtjSn3ra6CW6PRlLH43L17N+vWrSMhIYHAwECbxXr37l06d+7MtWvXbHaN\nGo4QaQsQIl1NcBZDlXPnzrNgyUf8XdQOpcaLopxfadik6mpjY7l9eQmh/eP0cWrUSu5mHMNN8zvh\nnZsRPWksjRqZbnFpDBX12+r+zZGFUlWhVqtZsfoDvvhqH33HrsPXz3hDGWVpEfkXV/LuSuvN/jaF\n+99btVqtH2wjlUpRKBTIZDI8PDz0XQ/vvfcep0+fZvPmzdSpY32/c0POnj3L5MmTCQkJITk5mS5d\nurB27Vo8PW0/vayGIETaAoRIV1PMrRq3Vmr8m28TmTlzCV6+3XD36Ym7V4DFrynv71+Ru2XStG0k\nBbnXUGR/RxM/LRPGDaNH9642FcHyBjJU9f32KpQyhf98/S3b/nOc1r1m4u7la9QxKae3EBv1KO3a\nlV+EZm90oq1QKFAoFMC9wrD333+f3r17s3v3bvz8/FixYoVd6gROnz5N9+7dOXHiBOHh4cTExODj\n48PChQttfu0aghBpC6jxIp2YmEhMTAxqtZqoqChiY2MdHZJNMDY1rhsQYmn6VqvVolQquXz5Mt8d\n/Imzv10jI6uUIkUALh6huLqbPmHo5oX5PPRILxp4/UXvHm2ZMH60zVdJ8L92HsPVmqmUt59tb7cu\nndFKVlYW85a8j2fQ0/gHd6/yuKvHZrD54yU2jc1UDCeKyeVysrKyiIuL48CBA6SkpNC1a1ciIiJ4\n8skn6dKli01jycjIoHv37ly/fh2A48ePs2zZMvbs2WPT69YghEhbQI0WabVaTevWrTl06BCBgYGE\nh4ezY8cO2rZt6+jQbIq5qXGpVKofEFLZStDQ5cmw6lmr1XLx4kW+3nWI85dukfmXkhJ1MC4ebdGo\nS1GW5iDR5uIizUOivYvcRYWHuwx3Nynu7jIUpTnMmflymX15W2POeEljsLdb1/1GKwDr1m/mxG95\ntOrxClJp+SvOzLT/8liTy4x7YbRV47GE0tLSB7Ycrl69yosvvsiCBQvo2bMnx48f5/vvv6devXrM\nnDnT5jH17t2bDRs20KpVK+bPn09xcTHLl1dc3CgogxBpC6jRIn3y5EkWLFhAYmIiAMuWLQNg+vTp\njgzL7lgzNW7KqlOtVnPmv79y8OAJ6vh4EdysMYEBjfHz86NRo0a4u1tvApepWDJe0pxr2XI/u7zJ\nTzrOnTvPguWfEtxtGj6+TR849sLhuWz+YIZTDNIwtFw1tPg8ceIEM2fOZNOmTbRr184hsSUnJxMV\nFYVCoaB58+Zs2rRJVHcbjxBpC6jRIr1z504OHDjAJ598AsDWrVv5+eefiYuLc3BkjsWY1Lhh+lap\nVAIglUpRq9X6VaeztSMZi7XHS5qKNfezjckEFBUVMWPuSorcwmgaMkz/9dKiu6hS17F8ieMfWnU1\nAUAZi8+EhATi4+NJSEjAz8/8aWACh1I9f1E4CbZbPjgB1VVEbI1cLqdXr1706tWrTGp8y5YtFabG\n9+7dy4ABA5DJZJSUlKBQKMoMCKku77Wtxkuagq5yWbd6N3wg0rUaVbWfXVHfcHl4enqydtU8vti5\nm537FtCmdywucndSf9vBkmnWq8w3F41GQ2FhYRmLT41Gw9KlS7l27Rr79u3Dw8PD0WEKBA6hRot0\nYGAgaWlp+r+npaXpRUdwD4lEgq+vL6NGjWLUqFFlUuOxsbHcuHGDwsJCgoKC6NevHz4+9yYq6VaC\nOkeu6jDSUOdWZe39Z0uRSCTI5XK9g5Zhary0tBTggdS4rhLd29vb6EzA6GeG0+2xzsTOnY5/h2hc\nlakEBwfb6mUZhaHFpy47U1JSwtSpU2nZsiXbtm1zmn50gcAR1Oh0t0qlonXr1nz//fcEBATw2GOP\n1YrCMWuxd+9eJk6cyKhRo/D19eXHH3+sMjWuc5NyJtMPR4yXtBbl7WfDva0HNzc35HK5yQ9EKpWK\nhW+/S/fHOjNkcIQtwjaK8iw+s7KyiIyMZMKECfzrX/9yyoc9gcmIH6IF1GiRBti/f7++BWvSpEnM\nmGE9j+majFKpZNCgQSxatIjHH38cMK5qXJeq1LV5Odr0w5HjJa2Nzo5St+J0pv5sU6goVX/x4kVe\neuklVq5cSZ8+fRwcpcCKOPcN6eTUeJEW2I6Kqsb79etHr169HOI1boizjJe0BuW1JYFz9GebQnkW\nnwBHjhxh0aJFbNmyhVatWjk4SoGVcZ4bsBoiRFpgNUytGrdVatwZx0uai6mpenv3Z5tCeVkNrVbL\n5s2b2bVrFzt27KBBA9NNcAROjxBpCxAibWfS0tIYN24cmZmZSCQSoqOjefXVVx0dltUxJTWua/My\n9Gw2NzVekdFKdcTSVL0z+Y3r+uvlcrk+q6FWq5k3bx65ubmsX7/eqYr5BFZFiLQFCJG2MxkZGWRk\nZNCpUycKCgro0qULu3btqvHFbOamxmUymd4FrarUrU7UpFKp2faezkJlBiXm4ii/cd22g2FVfWFh\nIdHR0Tz22GPExsY6vLhQYFOq7wfRCRAi7WBGjBjBK6+8QkSE46psHYG1U+PltfJUV2xlVXo/9tjP\n1lVwG+6lp6enExkZyauvvsozzzxjs5+VWq0mLCyMJk2a8O2339rkGgKjqL4fRidAiLQDSU1NpU+f\nPpw/fx5vb29Hh+MwTE2N6/7oUuO6YR9eXl42tfe0NaYYlNgCa+5nV7SX/ttvv/HKK68QFxdHt24P\nzgy3JmvWrOHMmTPk5+eze/dum15LUClCpC1AiLSDKCgooG/fvsyePZsRI0Y4OhynwtjUeH5+PoWF\nhfqBErrUrVwud7qq5qowdVSmPeIxdz+7vNei1WrZv38/a9asYfv27TY3Ubl16xaRkZHMmjWLNWvW\niJW0Y6k+H0QnRIi0A1AqlTz11FMMGTKEmJgYR4fj9JSXGu/UqRN79uxh7Nix+vGjzmyoUhk6W0xL\nRmXaGmP3s8t7LVqtlvXr13P06FG2bt1ql8EUo0aNYubMmeTl5bFq1Soh0o7F+W7oakT1zQ1WU7Ra\nLZMmTSIkJEQItJHc7zW+Y8cOXnrpJfr27UtiYiIXLlyoNDVeUlJicdW4rague+nG+I3LZDLUanWZ\nYjelUklsbCwuLi58/fXXdtmO2LNnD35+fnTu3JmjR49a/fzz5s2jfv36vPbaawDMmjULf3//Gtml\nIXA8YiVtZ44fP07v3r0JDQ3V/0JeunQpgwcPdnBk1YMjR44wbtw4vvzyS7p162Z0atzQBc1ZXLoq\nMiipjigUCoqLi5HJZCgUCgYMGEBoaChpaWkMGTKE2bNn2+09njlzJvHx8bi4uFBSUkJeXh5PP/00\nW7Zsscr5b9y4wciRIzlz5gwajYZWrVpx6tQpfH19rXL+GohzPnlWE4RIC6oVGo2G7OxsGjZsWO6/\nO4uhSmVUZy/x+zE0jtEVu2k0Gk6cOMHatWvJycnh4sWLNGnShMGDB7NixQq7PhAdO3bMJunugQMH\nsmLFCjIyMti4cSNffPGFVc9fwxAibQHV+/FdUOuQSqUVCjSYPobT3qlxQ4MSb29vp01vG4OhcYzh\nNK4zZ84wa9YsPvnkEzp16oRKpeLMmTOcP3/eYaNBrU1UVBSbNm3izp07TJw40ernFwh0iJW0AKgd\nPaWmpMYNXdCslRq3hUGJo9BqtRQWFj5g8blr1y7Wr19PQkICAQEBjg7TZiiVStq3b49arebKlSvV\n+mdpB8SbYwFiJS0AYO3atYSEhJCfn+/oUGyGRCKhZcuWtGzZkqlTp5ZJjcfFxT2QGndzc3ugQEqr\n1T7ggmYM9jIosQc6i08XFxfc3d312Yh33nmH5ORkEhMT9Q88NRW5XE7//v3x9fUVAi2wKUKkBdy6\ndYt9+/bpe0prC/ZIjTvaoMTalGfxWVpaSkxMDH5+fiQkJFT712gMGo2GpKQkdu7c6ehQBDUcIdIC\nXn/9dVauXEleXp6jQ3EYEokEX19fRo0axahRo8qkxmNjY6tMjSsUCoqKisqkxqVSqX71bbhnW10p\nz+IzOzubCRMmMHr0aKKiomrFqvLChQsMGzaMkSNH0rx5c0eHI6jhiD3pWs6ePXvYv38/69at4+jR\no6xevbrG7klbgjlV4xqNBolEgpubm94FrTqiywYolcoy1egpKSm8+OKLLF68mAEDBjg4SoETU/Of\n3GyIEOlajq17SmsiVXmNX7lyhfj4eD744AOkUqneqctZDVUqoyK70uPHjzN79mw+++wzQkJCHByl\nwMlx/hvdiREiLdBjq57Smo5havzjjz/m+vXrPPvsswwcOLDc1LjujzMYqlRGeaM/dY5v27dv5/PP\nP8fPz8/RYQqcH+e6sasZYk9aUAZnE4rqgEQioVmzZpw7dw6VSsUvv/xCVlaWSVXj94+JdHTxVXnt\nYhqNhiVLlpCWlsa+fftwd3d3aIwCQW1ArKQFAiugVCpZvHgx06ZNw8fHR/91S8dwOiI1Xl67WHFx\nMVOmTKFt27bMnTu32u6vCxyCePK3ACHSAoEdKc9QpUuXLvTv39/hqXFDi0/DCu7MzEwiIyOJiori\n+eefF9kWgamIG8YChEgLnJbc3FyioqL0dpIbN26kW7dujg7LqhhbNa5Wq/UDQu5PjVtjdrahn7iX\nl5d+pXzhwgWmTJnC6tWr6dWrlzVe8gOkpaUxbtw4MjMzkUgkREdHi4lSNQsh0hYgRFrgtIwfP54+\nffowceJEVCoVhYWFdplF7CjMTY0Degc0c1LjugpuQG/xCfD999/z9ttvEx8fT4sWLaz7Yg3IyMgg\nIyODTp06UVBQQJcuXdi1axdt27a12TUFdkWItAUIkRY4JXfv3qVz585cu3bN0aE4DHukxjUaDYWF\nhWUsPrVaLRs3bmTv3r1s376d+vXr2+slAzBixAheeeUVIiIi7Hpdgc0QIm0BQqQFTsnZs2eZPHky\nISEhJCcn06VLF9auXYunp6ejQ3MYpqTGdQNCKkuN6yw+3dzccHNzA+5Vdc+ZM4f8/Hw+/PBDu/uM\np6am0qdPH86fP4+3t7ddry2wGUKkLUCItMApOX36NN27d+fEiROEh4cTExODj48PCxcudHRoToEl\nqXFdSlyhUODp6YlcLgegoKCA6OhoevTowZtvvmn3Cu6CggL69u3L7NmzGTFihF2vLbApQqQtQIi0\nwCnJyMige/fuXL9+HbjncLVs2TL27Nnj4MicE2NT4yqViszMTP0q9fjx4yQlJREeHk5cXByvv/46\nTz/9tN0ruJVKJU899RRDhgwhJibGrtcW2Bwh0hYgRFrgtPTu3ZsNGzbQqlUr5s+fT3FxMcuXL3d0\nWNWC8lLjPXr0IDk5GZVKxZdffolEIuH8+fN8+umn7N+/n+zsbPr168eAAQMYPnw4wcHBdolVq9Uy\nfvx4GjRowDvvvGOXawrsihBpCxAiLXBakpOTiYqKQqFQ0Lx5czZt2lSjq7tthVar5cqVKwwfPhxX\nV1e8vb0JCAggIiICiURCfHw827dvx8vLi8OHD/Pdd9/Ru3dvxo0bZ5f4jh8/Tu/evQkNDdWv4Jcu\nXcrgwYPtcn2BzREibQFCpAWCGk5RURGhoaE8++yzLFiwAIlEQkpKComJiWzdupWDBw+WcUkTCKyM\nEGkLECItENQCzp8/T7t27RwdhqB2IkTaAoQBr8BoTp06RceOHSktLaWwsJD27dtz4cIFR4clMAIh\n0AJB9USspAUmMWfOHEpKSiguLqZp06bExsY6OiS7s3TpUrZu3YpUKqVDhw5s2rRJ32csEAgeQKyk\nLUCItMAklEolYWFheHh4cPLkyVo3bCE1NZX+/ftz8eJF3NzcGDNmDEOHDmX8+PGODk0gcFZq1y8J\nKyPS3QKT+OuvvygsLKSgoIDi4mJHh2N3fHx8kMvlFBUV6R27AgMDHR2WQCCooQiRFpjE5MmTWbx4\nMc8991ytTHXXr1+fadOmERQUREBAAPXq1eOJJ55wdFgCgaCGIkRaYDRbtmzBzc2NsWPHMn36dE6d\nOsXRo0cdHZZduXr1Ku+++y6pqan8+eefFBQUsG3bNkeHJRAIaihiT1ogMIGEhAQOHjzIhg0bAIiP\njycpKYl169Y5ODKBwGkRe9IWIFbSAoEJtGnThqSkJIqLi9FqtRw6dIiQkBBHhyUQCGooQqQFAhPo\n2LEj48aNIywsjNDQUACio6MdHJVAIKipiHS3QCAwicTERGJiYlCr1URFRdXKAkKBSYh0twUIkRYI\nBEajVqtp3bo1hw4dIjAwkPDwcHbs2EHbtm0dHZrAeREibQEi3S0QCIzml19+oUWLFgQHByOXyxk7\ndizffPONo8MSCGosQqQFgmrMxIkT8ff3p0OHDvqvZWdnM2DAAFq1asXAgQPJzc212vVu375N06ZN\n9X9v0qQJt2/fttr5BQJBWYRICwTVmAkTJpCYmFjma8uWLQxRE14AAAFKSURBVGPAgAFcvnyZiIgI\nli1bZrXr1TYbWIHA0QiRFgiqMb169cLX17fM13bv3q33Eh8/fjy7du2y2vUCAwNJS0vT/z0tLY0m\nTZpY7fwCgaAsQqQFghrGnTt38Pf3B8Df3587d+5Y7dxhYWFcuXKF1NRUFAoFCQkJDB8+3GrnFwgE\nZXFxdAACgcB2SCQSq6aoXVxceP/99xk0aBBqtZpJkyaJym6BwIYIkRYIahj+/v5kZGTQuHFj0tPT\n8fPzs+r5hwwZwpAhQ6x6ToFAUD4i3S0Q1DCGDx/O5s2bAdi8eTMjRoxwcEQCgcBcqjIzEQgEToxE\nItkB9AEaAneAucA3wBdAEJAKjNZqtdbrwxIIBHZDiLRAIBAIBE6KSHcLBAKBQOCkCJEWCAQCgcBJ\nESItEAgEAoGTIkRaIBAIBAInRYi0QCAQCAROyv8DCxbkkZKA8qQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f188f574a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib as mpl\n",
    "\n",
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=mpl.cm.coolwarm,\n",
    "        linewidth=0.5, antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_1\n",
    "# title: Function with two parameters\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "uuid": "5918f2cf-3ead-4b80-980e-4a375ee159db"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((len(x), 6 + 1))\n",
    "matrix[:, 6] = np.sqrt(y)\n",
    "matrix[:, 5] = np.sin(x)\n",
    "matrix[:, 4] = y ** 2\n",
    "matrix[:, 3] = x ** 2\n",
    "matrix[:, 2] = y\n",
    "matrix[:, 1] = x\n",
    "matrix[:, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "uuid": "48ce242e-3411-41bf-b6c1-c8e228f3e494"
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "uuid": "b9eb74bd-9280-4d8b-ae7d-8853911389cb"
   },
   "outputs": [],
   "source": [
    "model = sm.OLS(fm((x, y)), matrix).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "uuid": "cc9c9f77-9051-4d82-bb7b-c646216d542f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "uuid": "b68898de-9001-4a15-a5ee-7ee50c5592ea"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  7.14706072e-15,   2.50000000e-01,  -2.22044605e-16,\n",
       "        -1.02348685e-16,   5.00000000e-02,   1.00000000e+00,\n",
       "         1.00000000e+00])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = model.params\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "uuid": "1f5d1574-8238-45e4-987d-bdb7cc6b5e03"
   },
   "outputs": [],
   "source": [
    "def reg_func(a, (x, y)):\n",
    "    f6 = a[6] * np.sqrt(y)\n",
    "    f5 = a[5] * np.sin(x)\n",
    "    f4 = a[4] * y ** 2\n",
    "    f3 = a[3] * x ** 2\n",
    "    f2 = a[2] * y\n",
    "    f1 = a[1] * x\n",
    "    f0 = a[0] * 1\n",
    "    return (f6 + f5 + f4 + f3 +\n",
    "            f2 + f1 + f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "uuid": "fd9f8eed-1b10-4ec8-8a15-bedae7f53a18"
   },
   "outputs": [],
   "source": [
    "RZ = reg_func(a, (X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "uuid": "096451ce-173a-43b5-b81f-9dac26df2702"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x7f18742aa488>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F/EPguHFuQQLbBxtg5M3aVsibBR0SEuIT96L/qjHZ0ev1AOh0OsLDwwOuyQFc\nF3vnbHhljs8+c4GOtf7MV6BPppSg/cwW1HhxLEZVIts/WMfGtw/y5+GGfDpoh9fzUgfZmf1HGI0r\n7+LCh5/Tub6BTl9N4a6Fd3El2zcLqiidgTbldhIkG+l8p8Sbb6YSQHVt/EJSEtzZPonHhtl4NuEd\nvm/2glsCDbD8YmPUskQ7yTcCDbDSfgchKj0ttJ4JNECC+gJfRQ6mTNJG6tXOYflyg0/m5O+yoILA\nQ7i73SC/rG24vrK12Wx+6Zus7Kv2FXkTw4AC92kXFW/d3coiwmaz3dBg5OpViTVrSrPvpSU3nLfp\neCnGLGpAUnpT7m2zix9fW06ZmOsNLobOiKVO+cPUT7hW5HkpZBq1rN7fk61TviFUa+X9IfuZfM9J\nHp/XgEafTqNH9SW833MHoZqcIl/DZpf4cu99LHhkJYmxeu75+D5Wr7jEshXxlCzp9Uu46TiLjdUK\nY59M47vvouleeisftPmWkCDPtqS9//dABsizkVTXrWo9kVwlnvP2UhynJOcoRaq6HFaCaWDdQ0/2\nkqg6na8rWpZhkTSKkSFziuyuVktWJoR9wFbTNkYOm86yu5P5/IsyFPU24eo3ZTKZAq4FqcC3CJEu\nACULVck+zVvOE64XeAgPDw+oxBxXOMfKFeFTXleg4LyI0Gq1Lt/XFyZdom2185SP+XdzapohhJ4f\nNOOfy015/O49TOy3lIjQf+OX2UY1y7Z24I+JC3wyzye+qUz9CoeoXf7fjO74KAM/Pb2N48lHGfZ5\nU2p9cDcjGn/LpDsOEKTy/D3+eHttosMy6VrnApIEh16Zx2Nft6Ze3Whmf2Hl7rtvjxvzli05DB9q\n4Mq1EHqU/onXas/z6HyTLZgphx4gw1KbRer7mS+PJcdeGkmyEapOJkJ3mVK6K5TTXaVF6Hk0kp1N\nV1syLvMJrHYdsaptNLJupyd7qaA65RDkzfZmyFIEnXWbvH6NbXQ7qa25j8lr36B+7WBWrImmWrWi\nOzGdfxN5i5sIbj9ETDof8naqUn4YFosFg8HgsHLDw8P9lgltNpuxWCxeubMKipWnp6cTERHhc1e3\nxWLBaDR61KvaObs8LCzM5XualGSiVk0VOyd/TKVS6QB8+Gt5Xl35AB0bHmfB+H9yibPC4LdiOXWu\nFH9MXFf0F/V/Mo1aKo4bw9Yp3+QS6bxsPBrPyDltyTBoeKPTIvrVO5XvsXmxyxLV33+Bjx76nb6N\nT+f62/Is73qvAAAgAElEQVS9iYz85kHu6pXGJ5+VdssqC8SYdFqanUeHXWTr1ngebbqaT7f15Pc7\nBhCmvrGEqyvO6+OZerwr+9Pvw26XaVVyGw9V/I2yodeI0111a5yLhng2pNRhw+W6HM9ogtUeQkzQ\ndhpZt/Gn1IcHQ37igbCV3r5UB7IMXxn785NpDK+8ls3o0Z4Vb1fyM8LCwv4/nkyPHj3YsmVLoBsJ\nAT25QEeIdB7yc20rnZ8sFovDtZ2ZmenoWuUPvE3Acq4PHhYWdoMYZ2Rk5CuI3qBc152+tp4k3D0y\n/Bzndl9g9dh1JKWF0e2DtqQbqrJg/Ha6NHEtmFkGDeUH3MMfE+dTt7z3WdiDv6jF+fRENr34e6HH\nyjIs3FqBZxd2pUbJbfzUbzUhmoIzlAHm7a7BrL/u558357l0tV7JDKX3Jz1JtcSxfEUUNWoUbEkp\nBUQCQaRlGebMyeLlF3W0SPiL2X3X0Xtee6qqr/Jq7a8LPNcuS6xKbsjHZ+4hzdSYOyv/SvfKp5i0\nYTCbOz9McFDh721BJBvj2JBcm58utOPvrDsoF7yS18M+pJzGvbi4uxyzVOMl/SxqN7CwZGlZ3F3L\nuhLpnj17smXLFp/Ozw/4XaQlSQoYrZJl2aevV4i0E0piWF7Xttlsxmg0EhwcTGhoqENEMjMzCQkJ\nCTiRVoqoFFYf/GaLdGGLiNxzhQoJZrZO+JSvt0fzye/3c/8d+/h4zGl0wbZ8zxs0PZYzF0qyaYL3\nJUCzTMFUeH4MW6csLNCKvmHuBi33vNOOYxfj+O7+z2la/nK+x8oy1Pzwed7su4PBrf4u8LjXVzXg\ngw09eeHFTMY+VSLf2KnyndZqtW7P2R+cOGFnYL+rpF2R+Pzeb2lf+RwX0qNo+v4LrG/3ECWCXdfX\nzLSE8/aJjmy48gAhGhMjG//K8Ea7CdXk0GzOcHrG7ePJGqt8Ns9uGyfRo/xJMixalp+5j3ra73gp\nbAHhqiyfXcMohzAo9Uus6rJ8vwQ6dCj8s7HZbJjNZkcMWrGkt27d6rN5+YliEelVITX8fZlCuct4\n3OciLWLS3OjadrdTlb/LdhZlfE+KqNyssqOyLGM0Gh03HHeS1154IYkapS9z14cdkaUYfp2xnmY1\nCm4xmWXQsGJbR7ZM+son8x79dWXqVzjskUADRIWa+f2FX3lvbTX6fDeZIfW/5o0uu12K6o+HqyBJ\n4TzU4p8Cx5QkeKnXfnrVu0jftx/g++9S+OLLOOrUCbz4pNkM4567zKLvSvJI06289NA2NEHXF1Yj\nf2xEu1IrXAr0kYzyvHK8D6ezulM3/i8W9PmSVuX/jRvvSirDVX19RlSd6bO5HkhLJNXUkLF1PkSn\nzmFs7V8Zt7M//a78TFftx4wOX4ZaKryyXWFkW0Mx2hN5OuE9HrzvSR548BLvfxiPJ+tlm80WkLsy\nbhZBIQHwXrgXrfGI/7RI59epyl1LNBC6VCkoiWE2m83rIireUtD7YrFY0Ov1BAUFuV2JLT0d5s2N\nR5JiGHX3X0wbvh91UOHv+6j3I6mfeJDa5bzP6M4yBbNyf0+2TllYpPMlCZ7pcZJu9a5w18we/Hqm\nLmseWkxsnjaaL2/syaQef6ByM9msUYWrHJ36Ba+uqM+dHbrStMlFPvm8LBUq3PwwoNUKX3+t55WX\nISHiEtuemE1i9L8LnGv6cHZf6MnK1g/nOi/bGsrTB/pzML03D9ZZyQ+tJlAq7EYRf3JtZx6s8B26\noKJn0edl8sH76VdlCTr19THjQ9NYcMenHEpdzfM7hnJf6hAeDplBn5AtXhUpmWHsT+tSKxmQ+Cud\n4vYyeuVE6m1Qs3xlNNWru/5NuCpkori+BRAUEngLVF9we74qNyioU1V6+vWkJHc6Vd1sS1qJ6WZm\nZjqsZ08EurgWGUrxiuzsbEJDQ4mIiHA7K/WVKUlEhKay8+NVzBxxxi2BzjRoWLm9I588tNvbqQNF\nt6LzUrt8OsfeXkyDShYafzaFFccqOP629kQFcqxlGNH+hEdj6jRWpvXdw4nX36O8/QRNm8DA/klc\n8b5/SJHIyoIpU65RMdHE21Ov8VaXb/htxFe5BBpg9NJ6NIreQHzI9UWULMOcU23o/Md8NKGl2fno\nZGZ0XudSoA9fjiM5sxmjq3lXmMaZk1llSdG3Zmyd9Tf8rW7MWdZ2n8r05p+xyPIM/dO/YI+5ZpGu\nk22P4LC5P+Or/ARAnO4a3zceTxfdj7RpJfPOO+lu7YnPzs4WIu2ESi3d9Ic/+M9Z0s6JYYrlrJTz\nVLKL8+7NzQ9/Z1QWJtLO7vjIyEiPXV/+nL/zvBUXvEaj8biOeVYWzJ8fyx9vr6ZmQv7VxfLyyKwo\nGiQeCAgrOi9ajY1FY/5i8bYkRs0by5IjK5nbZxMTfu3GM102og4q2t74EqEmZg/+k6m99zNmUQtq\n1ypLv36XeHVqNMVR7+LiRXhxcjKrVpWmRtx5vr5/E20qnXN5bJZZy6Z/evN9y9HAddf2UwefRJZi\nmd/nI9pXKDgb/vHVHbknYQmhapPP5j9hfx96V/yJcE3+PstuCfvpXO5p5hzvwJQjH1PatJWZYTMp\noXY/Xv1edh/qlPiDMiH/5iaoJJknKy+lU8m9PP3WFJb9mMzSn8sQG/vvea4saVHI5F+EJX2Lo4iz\n2WzOJdBwvfxmZmYmwcHBREZGum2J3syYrsFgICsrC51O59U2Kn+1lITr3ors7GwMBgNhYWGEhYV5\nvKfzpReTqVfpOHUrud+0NzVLy7pdHfl8iOeVolwxckEVn1jReXmw1XkOvzWffzIbUvuD8aQbazC2\nU8E1ot2hdJSeH0b9xl+TPuHEtiRq1wpi6qsZmHynZ7nYv99O9y4XaFhfIvvYcf4YNY0NI77OV6AB\nxq+sS7XIHcRrUxm5dygP7/6IgfUPsvex1woV6L9TS3E2vR1P+zBZ7Fx2HGezOjOu/tpCjw1S2RlZ\n6zf+7P0Y1ePMDE7/gU3GBm5dxyxr2ZYzjIlVbyzGA1A78gwrmo+k5NUd1K1l5uef/61UJjpgFYwU\nJN30xw1zkqS5kiRdkiTpoNNzMZIkrZck6YQkSb9IklSioNf1nxBpZ9c24Ohdq5SdtNvtREVFeVxv\n+2YkjuWds6ftL/OO7w+UHsIZGRmoVCqPXfAKmZkwf34MH4/JP8vZFYOnl6B11d1UL+29qKbpdaw9\n0JPPh+/zeixXlInWs/eNn7FLWnJsoXzyu+9qMFeJS2P9M6v55akv+W15KokJFvo9cIE5c/ScOiV5\nVWbUbIYVK8w0aZhC985WarKHQ8++yML+K6gcW7D3wmRRs/xwH+pHHOHOzV8h68qz45EXmNhmE2pV\n4V6EUava0aPcT0Ro9EV/AXkYf6A3XRN+JirYfW9NmMbEh62+YlrzD3jb8C4vZ43AJhe8WP5S352E\nsENUjziT7zHaoBzeqvUZr1Z9lceGSwzsd5GsLIvjd6UgSoLmJkijuukPF8wDuud5biKwXpbl6sCG\n//9/vtzWIq1kbZvNZkcrScW1nZWV5bDwwsPDi1y1p7gsabvd7rM5+xMlbAAQERGRa8uap0yelEyD\nyseoW9F9V2LyNS2bD97BZ4N9E4sePq8qLarup2ZZ31rRzmw7GY3VFsXy19by9vo+tJvRDr3Zd4l/\nDROvMHfIBmxWNfHGE8z74AztWpuIj5No0jCJkY8ls3RpDleu5P6c7HY4f17il1/svP56Kg/cf4HG\nDS+SWN5IXJyOR4dZGFT1V06Mf4kZPTcRHepefepnlrfEZg9i3dXezL37M5Y/uID4cPc8JefTozl5\nrRPP11zh8fuQHymGaE5k3MWk+kWzzHsm7mN9zydJ0TRnQPocLlhKuzzOJgex1jyC56t879a4HeP2\n8nPzoezYZGTJkmQsFgtWq5XMzExmzJjBoUOHPN5WN3z4cOLj46lXr57judTUVLp06UL16tXp2rWr\nIyfnVkMKUt30R15kWd4M5L159Abm//+/5wN9Cnxdt+M+aSVr22q1uizn6atOVSaTyZFN7Q9kWSYt\nLY3Q0FCMRiNardZnzTsAR5a1L4pcOO8n12q1mEwmYmJiijxeRgZUqGDmz3dWUauC+yLd8fmyRAer\nWfK4940WrmTqqD7pSfa+OY9Kce672z2l1vgO3N/ByBvDL5Bl0HDvKzXYdzKexY8toX0N33TWavFm\nG5pUlvls+F7Hc8lp4fxxrBRrDkSz+2wiF69WRas1Eh93lfSMMNIz4tBq9MRGXqRiycvULZtKiypG\n6iVmcMdrXZjRczX31z/m9hyMFg1DF7fitxMDuKfGaj7ovtixFctdei7qTZxk4u1G8ws/2E0e3j6E\nEiE6Pmn9lVfj2GWJGQfuZuHJfgwJeYV+YRtz/f07fSdW2QezulX+vanzkmGJoPu279m7X6JUKROS\nJKHX65kxYwbbtm3j8OHDVK9enRYtWtCpUycGDBhQ4HibN28mPDycIUOGcPDgdQ/s+PHjKVmyJOPH\nj+ett94iLS2N6dOne/z6C6BY9klvb9nc35cplJbbd9ywT1qSpIrAClmW6/3//9NkWY7+/39LQKry\n/6647RLHlFrbmZmZ6HQ6RyMJ560/RUmycoW/3d1K1TOloIm/yo96i7P1HBkZiUqlctQ2LyoTJybT\nuGqKRwJ97lIIu0+05egbn3h1bYUhX9bgjto7/SrQf/0dzeWMOrz40HXLMCLUwq8zDvHJ8ivc+8kI\nHmi2nE8GHnd7S5Yrzl6N5GRKe9ZN/CzX82Wis+nXKpt+rU4De7Db4e9Lsew7G0m10kaqxqcSEXLj\n9qYFm0ujVgXRt+5xt+ewYHclXlg7iHBdFmUjD/HpXYs8fh3JWZEcvtSNdzoO9/jc/Eg1R3Eg7V5+\nbfW412OpJJmJDX6mc5kjjNo6ns221syMeJcQyYgsw2LzCCbXmOvRmB+fvpsmjS+QkJCAyXQ9VBcT\nE8P06dOZO3cuISEhNGnShO3bt3Px4sVCx2vXrh1nzpzJ9dzPP//Mpk3Xa5QPHTqUDh06+FqkiwWV\ni5hwoCPLslxYtbTAvOsXEaVBg3OChVLO02q1Okp4+soS9ZdIOxf7ADzaruQJ3s7f2TMREhLiiI8r\nY+ZNdHGX9HRY9G0s29/f5tF5D75ekt6NN1O6hPexyqS0MLb/3Y3DM+Z4PVZBDP+iPiPv3k2INrdF\n+cQ9l+jWdC3dJrai1pQabHxuPWVKFK3d4cNf1eCuRn8SE17wwkmlguplrlG9TMEx5ReXNGPCHevc\nWjhcSI+iz4JupBpq8vljG3n8i7Z80qNoVvBjq9rTPn4VJXW+c8dOPtCDZnEbKB3qu17gTeP+ZmOv\npxi5dQQDrn3LaxHPk2KNJUiloWuc+61STbZgVl/qx4bFrm/TBoOBsmXL0qRJE5o0aVLk+V66dIn4\n+HgA4uPjuXTpUpHHupmoNMVfzGRXWga70wsuquSCS5IklZZlOUWSpDJA/iUIuc1i0opbWxE0JclK\nSV7yR1tGX4t03sSwQC2cr8TGlB7azqEDb+c8YXwSTasfpkaC+1b0sbOhHD3Xknf77/fq2goPfVGT\n7g23US7G/UQiT9n5dzQp6XV5eVCSy79XKafn6Lwt3NnESN0pjzNvi+dJZZcyQth/rjNvDzzs7XQB\nWLm3FDmWkgxteqjA46w2FWOXN6HZB5NpVzeHM59+z6nLViK1GXSu5L4FrpCcFcmBlB5Mrv1TUad+\nAxk5Eey4+iBTGy/z2ZgK4RojCzt8wNi6i5mYOZcPDJN5NHGhRwVQvjrXlUqVr1C37vX7Wd5Fb1ZW\nls+zu513vdxqSCqp2B/NYkswqkoFx8NNfgaG/v+/hwIFfgFvK0sarn/JlASL/Mp5+vJaviKvxe/c\nm9pfLvWiWNLuVmMrKmlp8P33JdnxgWdWdP9p8QxouYmYMO/r8p29GsG+s504Pna212MVxLA59Rhx\n1x5CdfnHZTVqmS+ePUXftmkMmtafRbv+5KdRewnXuVdl69EFNbij9l+UifZNJvTTCxrwZJu1Be7l\n/uV4WUYt7U/JKBN/TfueWuUzsNvh7Z/b8E7n74tUqUuxokvpfJfAN/lADxqX2kRCeIGGjFc8XOMP\nwtQ5vLR7Mt9cvJMucbsppSvc8rLag/guaTDf/hDieC7vb9VX+6Tj4+NJSUmhdOnSJCcnExcX5/WY\nN4N8sqtvKpIkLQLuAEpKknQeeBmYDiyWJOkR4AzwYEFj3HYibTAYMJlMqNVqgoKC/BrH9YW7O2/C\nVV7rOZBWtUpc35O64J7Of/y4JJrXTKFaefct2L1/h3EmuQm/P/sROdYgzqdGcTQpnD9OqDhwIYwL\n6aVIN5RBllVUKXWEfs1Tub/JNeKjXF9jwOza3NtsC/FRRXMvu8Puf0qQnFafKUPcy1Lu0TyNE/PX\ncf+r1ak4sS0PtfiZmQ+cIlidv8CnGULYerI7e9/0rEdzfmw5FkO6viqjW7su6pJmCOW+bzpw4kob\n3hywgVFdzzoE+eO18YSqc7ir2hGPr6tY0Ws7PuLN9HORaQln25X+rOr2lM/GzI9PjrdnbIuvSM6O\npPdf83im8us8mLCnwHOWJrWlRKyJO+7I3SIrbzETX1jSvXv3Zv78+UyYMIH58+fTp0+BycYBixSA\nu11kWc4vk6+zu2PcdiKt0WjQarWYzWa/b4/yVqSdq5zlZ/H7MzlNacFZGAVZ+b7k2jVYsqQkuz76\n0+1zDp8O585xbZCkbKpMHIE5J5bQkFRKhF8mIT6LGtXM3FvFRoOqF5FlmR9/j2bOtkq8tLQamqB0\nysccpFe9JAa3zqBKXBonUiI5ltSOVeP8a0U/PKcuj/TcTZjO/WYNsZE5/D7rEDuPnePRdxpTfnw3\nnu60kgk9zhLkIj48emFlmlTZ57PEt5Fza/NI8zVo1bnnfCE9itHLG7LjbE861d/NL69+Q1Tov5a+\nLMPrP7bg9TuWBY4Vvb8HDUv+QYUI/8Zf911LJM1Uj6dbLECnttCn+hEeWzWelVf/4PP6XxISZL7h\nHFmGOReG8NaHEXmev7GYiaeW9IABA9i0aRNXr14lISGBqVOnMnHiRB588EG+/PJLKlasyOLFi4v2\nYm8ygWhJ+4LbTqSDg4Mde6LdESBvKYqAOieGOSdcBRrKPnO9Xk9wcLDfY+RPj71A27rJVClbsGtW\nlmHF9kienZ3ApWt1ATXfvrKdulX0lCtlQKPO/zNpUx/gMnb7CQ6fjmTZH1rWbq/Hp5sqY7OrsNuN\ntK52oNAkK2/Yd6YEF6814pUhPxfp/GY1M9k/ezfrdsYw+oMOfLQxiNd7r2VY24sOEcw2BbPukO9K\nmR44F0VyWkOev+Pf8Nn2s2V4ekULzqa2oUvDHewbs4jKpW/MI/hyQyk0kor7ah284W+FkZwVyf6U\nnqzzYUZ3piWMbVf683PXZ3w2Zn5M2HkPg+uvQKe+XkipY6V/2D1iCoOX9afrn5/zTp2pNIvJXWHt\ntytNkIPDuO++EFdDOiiKJb1okeus+l9//dWjcQIRSRV491BfcNuJtHPyUnFY0p7iaRcof1vS+Y1t\nt9vR6/XYbDa3a5m7O7YrkpJkfl4Rx8HZ+ceirTaJ936KZNaP9bHLUTwx5CJffn+aUb2v0qutZ90k\nVCqoVyWTelXgpWFXkOXTrPozhgFT2rLzdDA1x6tYPGY39RM9ztwslCGf12FY992Eh3jX8rBbs1RO\nLtjCot9KMW723UxdncYn/TfSs8ElnltSkVrljvmslOmw2dV4sME6QjU5LNhVhWkbO6LPqcCwjtt5\n8b55lAi70SKE6wuql75vxottlnthRa/0qRX94oHu1C+5lUqRKT4b0xUn0suQrG/NuNbP53o+Umtk\neb95zN3bhLF/vMOdcQuYWnMZQdJ1o+Kjc4N4fpKKvLcGV7W7IyNzu8P/y6jUAdCq0g/cdiKtUFwi\n7e41iuoyLu764Hlj5OHh4cVi5Y9+4jzdmyWRUOrGOHCWQcO4LyJYvKkNsdGZTJ+UyX09r/HDajtm\nUxmeH+h+QY38kCR4/sMIxjy4i5cfTWXK5zHc8fpQ6pTfwg9PHqV0tG8axe47U4IL15ow9eGiWdF5\nkSQY2OkK/Tps4OPl8Qz/egBRP/zNlczarB3vXmWrwjhzOYJ/UtrQqswSKk2fQJjOyqS+e3m00yY0\n6oK9VYu2lAJ7KP3rep517w8rOssSxtbLA1ne5VmfjZkfz+/sxX21VxEe7NorM7zRbjpXPsMDPwyj\nx/bWzG3wFlfMMaRaKvLYY7kLDLm6B5jNZr+Fnm5FhCV9C1KcbRjzEzJl77bBYCgWl7En5F0AuBMj\n9wdnzsj89ltpjs/NHYtOywpmwLQY/jzSntpVz7Dk8wu0anzdYrPbYeK0ON4YeaRA97a7rNsewtWM\nqrz86FZ0Wjtvjb3K+KFbGP1WDDXHP0aPhmuZ8+gpwrQWr64z6LN6PNJzFxGh3o2Tl6AgmbF9UxjZ\nazUdn6tNSrqWbm8NJTLsONXiTtKnaRZ9mmSREJtRqEVrt0NSWiSHz0ey/rDEgs2tsNm1bEtpwMKn\nNtO1QYpbVrEsw/ivG/F8y+WoCq7X4JLHVrUr1Iq22IOwyyq0Qe69ny8d7Ebd2K1Ujkr2eD6ecCE7\nltOZnVjadnyBxyVGXePPYbN4aWMX7t/xBVHB53l0pB6NxnUVwLz3jkC5lwQCwpK+RfDVXl1PrpWf\nSPtC9IrDks6vKIk3eDLvkSPOcV+7C8RHm/8/H3jnxwimLuxM6ybn2LbsBJUScm85+ugrCzqNmmF3\ned+KUpbhsRkVmTTsMDrtv5ZhbFQO372Zwt/n0xn2alUSxnbkic6refW+8y4TtQrjr7+jSU5rwNSH\nfVd3Oi+SBEfPV2D12xtoUMXA9sORrPwzhq+2VWLq0srY7RAbeZhGiWd5qLWJqFCJ9Qcldp4O41xq\nPOn68hhMCQRr9ERHJFO2ZDbGnIqsfXEJ7Wp5JmxL/4rFYolmaAPP66hfzIxif0ovPmj8OkvPNeVo\nZiRn9NFctZYiwxKHyRpHji2eHGsUKpWFSO1haoXvoH/iMVqVOu5StLMsYWy+NJDlXZ7zeD6e8uyO\nu+he9ReiQwrf+hakknnzzl9oUvoKz6x/nPETCv9uFbVQ0O2MSBy7xSguN7GrH4o/RM8fKMl1mZmZ\nRe5J7S1Hj9r4a0dpTi+4bkWfTdHS9YVqZBkTWPTRKTq0vPFma7FIzPy8KvMmH7ohblcUvlmnw2KN\nZWw/1y0SqyaY2DznLJv3XuPR11sxZ2NbZg1cz0NtPIuDD/28AY/33uVRRrenvPxVBOVKXqZ9g+ux\n9G4trtGtBUAysnyMC5dD+W1PGKu3JzBucSmsNhWJ8WnUqWKgf88cGlU/TrXyu4gIvT7Hzk9H073x\nVo8FWpbhqXkNebblMo8WNFcNkbz4e0NWnngIUPPS0eFEhaRSOiKdCuUz6RCTQbVSyVSKySY+IoNS\nYVmYrBo2n6rIDwcSeONEO67trUKk9iB1I3YwsOJxmsWeQKOy8vLBrtSJ3e53K/qyIZKjqXcxv2+B\nzY1uYNHRejw0MIXw8Pgb/uZKlIVQ5yYQt2D5AiHSPr6Or2uE+7P0qNlsdjQIuVnV2B4bcYEhXc4S\nGZrD059GM3dtZ/r3/pu3Jp9DG+z6/CnvGImPyeDutt6Xh7TbYfzHtZk25jjqQtzm7Rplc+yHwyxc\nE8Uz7/Zl3uYdrHruAFpN4U0i/jgWw9Ws2rw0aKXXc84Pi1Vi9qrWLHnN9R5cSYKEeANDexgY2gPg\nfIHjpVwLZueRdhx572uP5/LjthhyckoyvFHhPb1lGTacqsiUzW25kNGO+okHUElw4PkXiY8ofL98\nWHAO3WueoHvNE8AGssxafv+7Ij8cqMCLRzqTbqhApPYA6ab6LO5UDBndu7rRruJGtzt7AZzPiGV3\nUhu+fc3134UgF45KLUT6lqA4s7udr2O32zEajVgsFp/WCPfH61AWEiqVCpVK5XG7O3dw57Xv2WPl\n8KE4pj24l8TBLdHpQvl10Unq1si/mpbBqOKrJQ1YPesvn8xz1iIdIdoghtzlXha3JMGgnhnc1XYH\ndz+TQKVnarD2+dXUr1jwDfnROY15qu+NNbp9yWvfRBIfk8adTXxT23r49FDuqLuL8rGeVSuTZXhm\nfmOea7WswP7QWeYQpm2px4/He6JSaRnecTfP9/qcntOrc3fdX9wSaFdEaM30rnOc3nWOA7+QYQyh\n7/yeGC9nMGjjKzxSfTaj62wvUpy8MDJywtl1+T42D3vZo/Ne2NSJnj2TiIkp69bxFoulSD3ab2cC\n1ZKWJOkp4FGudwP7Qpbl9z05/7YTaYXiEmklMUzJtAykxLC8KAuJnJwcwsLCUKlUju5VN4MRj6ZQ\nOjqDni90Y+zwk0x4PLNQ9/WTLxuoVfEsreq6X9c7PyxWibe+acq8KUc93h4UHWlh85xTTP8qhvZv\nPMyTXZcy9f7zLsdZdyCWdH1VJvYvWr9id7DaJD5e3pJvp+zzyXjXMoLZur89B2d5vs/6h22x5Fhi\nGdbQtRW9O6kckza24PiVLtQqf4ivnthC9wZJSBKcTIrg6IV2/DAwH5OyiBxOacrWZz7gYnoojy+5\nn29O3cdrjWbTNeGET68zeVcnGpXdRmKU+7kSl7Mj2Xy2EwdX53+MLwqZ3O4EYuKYJEl1uS7QzQAL\nsFaSpJWyLP/j7hi3rUgr+NNNZLPZHCLtr2xoXy02lAxzjUbj2J+tzN8fFDbv1auzOXwkkRpVTrJz\n5THKlyk8TpuWoWbVhiZsn/OHT+Y46VMtpWMz6NWuaIIvSTBpWCo922yj1zN3snL/P2ycvJOo0Nx7\nhh+f14znH9yDNth/xXWmfRtBbFQWXZv7xop+ZHoIrWvuoUKcZ++NYkU/33LpDVb0nuR4hq/sR7a5\nMg+02s6yiXMpG5N7kdj/w2rc3/AXYkJ9t3gc+WMjmlbYTfW4a1SPu8bRyZ/z5bbaTFoziRmHDvNJ\nq9yGkbIAACAASURBVG+oXsL7PdPZllD+SO7Hr4Ne9+i8VzZ3pH37i5QuXc79awmRvpHANI5qAn/J\nsmwCkCRpE9AXmOnuALedSDu7u4taP7ownBPDJEkiJCTEr9uVvBFS5/3ZYWFhAeEik2V4/rlMHn4g\nibdfLHxLkMKQp/W0bXCMWhW8r6ltMAXx5co2rHi34BrK7tCgupETP+1lwAtlqPLsIBY+8RPd6l/f\nNrRidyn05gSee6DgrlHeYLNJvL+0BfMne17RyxXp2Rp+39OevTM87/m8+M9YLJaYXFZ0pjmEIT93\nYV9yV57rtYFJ92xAHXTjd/rguQj+udSS1Q+/6tX8nUk1hLHx73vY8dy7juckCR5tfYRBzU7w8upm\n3LfhPerFruLjVsuI1hbdQ/Pi7jupF7+barHulxpNN4Wx5u8e7Piu4ONcFTIRIp2bQLSkgUPAG5Ik\nxQAm4C7A/X6l3GatKvPir3iuc4tGf+8lLuoCQ0kMc27VmVegi7tQisLSpXrS03W8Ncl9gf7nrJqd\n+5syZ5JvMnNHzdRRs+J52jTwjcUWorWz7O2LvP30Mfp/NIhhn1fFZoMxC1oyeeBen+zlzo+ZiyMo\nEW6gRyvfVOV67K0QmlbdT5XSntX8lmV4bn4TxrX6iSCVjF2WeGtLI+p/Pp2QiHhOvDuPl/oedynQ\nAAM/rM2gJmuI1PmuJOujSxrTuvJ2KpW8sV+0TmNlxj3bODz5LaJjYmi/cjaTdnYlx+b5QlZv0fHb\nxQG83XmtR+dN29qOxo0vUqmSZ7/zrKwsIdJ5uBmtKvM+8iLL8jHgLeAXYA2wF/DIpXbbWdLO+FKE\nnOO5eVs0+lPoivIablZREmfym7fdDs88beKVpy/iybQGjrEwsOs+ysS6Lj/pCZfTNCz/oz1/feV+\nIw93efjuDDo2/ZNuTzYh8anG2OQonrx3r8+vo2C3w6wlzZg94bBPvH2Zeg2/7GjPX9M8b7Lw/Z+x\nWK0leLjBbradL8eI1QMJ1oSycvxPtK1Z8Ha1XX+X4MK1RkwZMbWoU7+BS5lh/Hm6F7vHzSrwuLgI\nPT8OX8OhpF08sqgLLVf05YMWb9G2zGm3rzVlT0dqxe2jZkn33eYGi5Yfjt7Nb5sKt5VcWdK+7iV9\nq3MzLOmt51L481zBnhNZlucCcwEkSXoTOOfJNW47kfaHaztvxTDnetuBlCTmXNJTp9Oh0+kKnN/N\nKDn64YdXUassDOzjvthu2i5xMaUmMz/93Sfz6P9yGHc2O0KNir4p9ZmXCmXMHFx0hPhubbHaQpi3\nNpQRd/knQe/9nyKICM3hnra+saJHvxNCg4qHqVnOs9i2YkWPabqauxffy9ErHZl0z6883+ukW3vZ\nB31Sh0dbrCJc6/0iTGH4kuZ0qL6VxBj3Xkvdslf467lvmbe9Jk8sf4MeCV8zrdnaQrPADVYtv1x4\niFUD3vJofu9sb0X16peoU6fwWHTe36mISd/IzSgL2rZiGdpWLOP4/1l/3hhykiQpTpbly5IkJQL3\nAi08ucZtJ9LO+KKVpMFgwG6359tkwt9C5+74VqsVvV5/04qSFIbNZiM1NZs339Dy2bRkt60+WYaR\nE8OZMGif1w0pAI6f0bH7WCuO/7TZ67EKYu7PGsJCTXz0+hkeHdeJ7zbuZvUbyT5NHrPbYdqiJnz0\n7HGfWNF6o5oVW9uy9bUfPT534eaSZBnLMWNbPzrW3cfKF+e53UnsjyPRXMmozaROnl83P5IyIth9\nvjv7J7qdn+NgWMtjdKz2HnfNfpA71zRhcYcPiAvN3/U/de8dVC95kDpxSW5fw2xVM//gvSxf6f4t\nWGR3F4wUYPc8J36QJCmW69ndT8iy7FEc6baMSXu7V1ppJZmZmYlarSYyMjLfhKviKttZ0N8MBgNZ\nWVlotVoiIiI8Fmh/zF95X5zfy/feM1C6VCpd27lvLc1bbMVqjebZAVd9Mq/7XophaK8DxMfkvxfb\nW2w2mDK7Dm9OvELXO6zsX3+KbHsCiQ+1Y+/JUJ9d590fIwgPsXF/hxvjrUVhzLsh1C5/nLqJnlnl\nvx0swcjP+xOmM7P+hSUse267R60+h3/egCdaryJE47t65sMWN6drrT8oG1W0XtoVY9PZP34OHWte\npvOaj/jhVB2Xx5mswaw+N5gZnTyLRX+2uznlyqXRvLl7Ii06YBWOpFLd9IcrZFluL8tyHVmWG8qy\n7LE7UFjSeSiKRepvSzo/lLkqiWGFtb30ZGxf4FxyVJIi+fSTEH6ee9zt861WePXdinz07OF8k408\nYcOuEJKv1mbamK1ej1UQ078KJjzczn09ry9GoqPsbPguk3dmB3PHcz14vNevTB/hftKcK2w2iemL\nmjF7/BGfWNHZRjVL/2jH5lfdt2bTsrXcPaMa+0+3RRes5+yHCzxOkFu9N5Z0fWWe6+B5Jnl+nE+L\nYv/Frhwa4pn7OS/qIDufPriRu+ue4ZGF41l1cS2ft15CcNC/Hp039rWnSuxRGpa+4Pa4FlsQn+7p\ny+x5sqM6YVBQkKO4kDu/S71eT4UKFYr0um5XpMDM7vYaYUn/H1m+/oPJyspCp9O5bZH6W+hcvYa8\ncw0PD/dYoP2JLMtYrVZMJpPDup848TL1ap6lUR33LdiXZ5koWULPA3d6v/dXlmH4mxWY+PAhQnX+\nq/qVY5F4d1ET3pmSnks8JQmeG5nDr4v+5ttNzak3oiZpWUVvMzjj+wiiwnO4p51vYtFPzAqhbsJx\n6lcsfDy7HV7+vjQVRw+mRMmShOou887gdR4LtCzDyDktmNDxZ7Rq39UzH/J9S3rV20h8ZNEqluWl\nZ+0zHJz0LhnUoN2qaZxIjwPAbNPw89nBzLhzjUfjfbm3GbGlDPToEYFOpyMoKAibzYbJZEKv12M0\nGjGbzVitVsdv31UxE5E4lpubndntr5i4sKT5t9CHWq322CIt7uQrb+bqCl/vJVese1mW0Wq16HQ6\nLl2SWbTof+ydZXgUZ9uGz1lLNq5EISRBgzsEK1asaKFYcS9Q3Iq7tLgVKRRK8eJS3KXFXQPBg4XY\nJlmd70feDQEiu8ku5OV7r+PYH9nMPPPM7Mxcz23X7cHJzS9NHidWJeX3DcXZM+t0qpaiwQARkUrs\nbXU4O2TsJl22wxa93o1+LU3P2M0Mhs6T4+sVRa3KqS9GCuXXcmnfM7oOtieobS1+H3SIRpXMS2DT\n6QVmbCrHiuFXLWJFx8bL2H68Cicnbspw29O3nfhudigyuT07513i/A01V2+60rbyQ7OP+/vRHOj1\nzvQMtYxKGsCdl67ciqjGli5Zs6I/hIdDPCf7rWHC3jJ8e3AOXfPP4a1aSYDrXUr5mp6sqzNImHuu\nKUtXJiV1Gq1oYzjNYDBgMBjQ6/VoNBoMBkPys6nT6dDr9chksixnd0+ZMoXVq1cjkUgoUqQIK1as\nsIo88KdENo5JZwn/r0namBhmbDKRGaGPT5U4lh1FSVLiw85fer0+eQHR64cnVKsQ+1G7yfTQdUg8\nBXI/JSFRwcQVSi7cMRD+woHXUW4kJHqToM6BQh6PVmeDvfIR+XPd4/vaBppU1eDh/P5xdHqBEYuL\nM2/w3QybaGQFqgQpK3dWYMtv6S8EbG1E/pibwKZdT2g/pg41Dp5kzfDXJieVTfrTETcnFfVDLWNF\n9/zFjqK5b6Ybi46JV9D0l2DOhlVmUPurDOmYRExNBxRiUcfjZi8WDAYYvrYKk+rszFTbz7TQdn0V\nWpbej7u95bPpBQFG1zlL/ZBHNFnWkVh1DlY3Ni8xbeXlkji5avj6a+dU/290eRvLJo3PfmJiIqIo\nsm3bNgYNGkRQUFByOKlcuXI4O6c+XmoIDw9n6dKl3Lx5ExsbG1q0aMG6deto3769WeeS3ZBdtbuz\nii/zrP6DtAjUSCjGxLDUhD7MgbUtaYPBQHR0NIIgZHmuH8ISiwydTveewIux9EsURe7eNXDggBez\nRpuWLHb9jozQJgL7j1fn9qOcdJqWm13nA7B1y0XDbzyYMdGOvZuiCDt3jfCLYdw/f5Pf5+soWMSL\nWZuCCGpWlxzflKN8NxdmrrXn2WslIxfb4u6cQPOapjXRyCx+mCYjf/AzyhY3LQGqWX0t53aHER4Z\nhM93dRm3ygm9Pn220+kF5m6pwJy+YRari955sjK/dk1dEU0UYdrWHOTq2QaUPtza9g/Du0QjlcLP\nv0twVibQtGz63bRSw887fLCT62lV4kZWTyEZ5x7n4HFkOSbVN0vQyWyUyvWCpsUOYCOPpsuujuwP\ny2XSfnqDwKyzTZky3dHk385obQuCgEKhoEWLFpw9exZ/f38MBgOTJk3Cz8+POXNM79lgTIQ1Lvrj\n4+Px8zNdkjS7QpBKP/vHGvgiLen0YtKWLlWyZkzaYDAkN8D4XKIk6cGYua1Wqz8SeDFe+w7tn9K6\ncRQ5PNKOOYoibNsHI3+xITIqL3L5G+rVvM7yuSmJXQBE4H3XsI1CJLRsIqFlBSARne4mV27Ysm1P\nDlYekDNueSBanZLWdY4jitaT930bI2fb0YocWn/PrP18cug49lcMh08l0HdMCRZslzCl0zk61Y1N\nda7jVjmRwzWaOuUso9HdbbotxQOvUyjn++MZDPDncU9GrCuOQXBjw4yrVC/7To5VqxOY9UdRVv2w\nz+xrqtVJ+HlHTZY1X2fR36Pzxup0r7QbR1vL1VqnhkStjHUXvmHH4K3cjVDSbdVgqgVuZUn9w+l2\n/VpztThKB/jmG1uzj5kyJOXt7Y1Op2PSpEm4ubmh1WpJTDQ9m97NzY2BAweSK1culEoltWvXpmbN\nmmbPKbvhf4lj/+VIWapkTmJYRrCGu9to6UdHRycTs7UIOrPzN1rPer0eZ2dnbGxsPlqwHDum5fZt\nN8YNSN3NrdYITJmvJbCiLwMmBvJdG1dmzYtEq3VlzuTMlePIZFCyaCLjhsLxnVqqhJ4jOCicQxcD\n8KtXlI0HrBMm6DBORpli4RTMm7l5VwvVcnnfK6aNiGTUqlByti7L7n/t39tGqxNYsC2UuX0tE1eP\njpPz95kqLO72zpqNV8sYtNIXr67f8dP6r+jfPo57O6+9R9AAYxcKeDm9oV5x82Vah631xdvxBbUL\n3M/yORhx8I4fkaoC/FQr61rsGWHY9gIE5nhIaL6XtK/ykGvTf+debEmKLx3IvTduqe5jEAV+/rcp\nE6coM7UwSU+7Wy6XmxWfDgsLY/bs2YSHh/Ps2TPi4uL480/zu51lNxj7NXzOjzWQvUwzC8NIQJZO\ntkrtGJbCh5KeUqk0OR6VHdTN0rOe398O+vROYHD3l9gp37cu3ryVMWBCLPuOlcTb5w3jp8ioVVsA\n7KhcLoqBPzzE0SHroh+Pnkg4dqokx/c9xc9Xz5oNAr2nlWXEooesn/ySEun0rTYHz1/JOXq+Iv/s\nzFrbQ0GA7xpo+bbeYxauUtB2ag3cne6ybsRDSuaNZ+RyR3w8IqlZxjJWdJdptpQMvkYBvyievLaj\n+1IfTtysQVCuh6ycFE6tCnGpEopaI2HJppJsGbDT7GPGq2UsP1yXLR0WW+AMkiCK0GtrbQbV2IOt\n3HJZ4qkhQStn7YUm7B32LsnO103Fxck7GLWxEDVWj+eHUssYUvHSe9du442iyJVymja1TJ28MYEs\nMzh37hyhoaG4u7sD0LRpU06dOkWbNm0sMrfPhf9Z0v9FSKmpbYy52NvbW61UyRIknVL0Q6FQJDfv\n+BwlXmnBFOvZiD//jEedKKFn23eux0S1QMteakJqFCIixpc1G9XsOeDA13VkCAIsX/oKqWBPr06W\nUeVq01NFo2/C8ffTIwjQpoXI5TOvafCNLdV7Via0szMRr7NuWTcfruTrqvfI5WcZMQ6pFPp01HDn\neBgNattQbVBdSvbIzeJdXzG/n2Ws6Kg4Ofv+rUrX6s8oMqgkIQPaI3P05cya85xd85ivQ1MnaICh\nM0UCPJ9QNcT0bk9G9PgtJ/lz3KJcwNMsnsE7bLqcG7XOmx+rXLbYmGlh8NaC5PEOo0zw++I6EglM\nanGdAz+tZdWN5lT9oz1RiUmeEFGEqaebMnaCTaat6NSQ2XdDgQIFOHPmDAkJCYiiyIEDBwgJCcnU\nWNkKguTzf1KbliAMFwThuiAIVwVBWCMIgllp9F+kJW10FyckJMUvnZ2drUZ2lhg3pShJanFya7Xc\nNBWmWs9GaDQwapScOWOeYDyVLX/r+XFMMLmDVOw9FIe3j+t7+6jVsHBeDpbOfIkl8i+OnDTw+GlB\ndm6MIGXTGRuFyMghEnp1e8aQkZ4UaBZA/UonWTpSm6n66at3bbgeVpb1S00XaTEVtjYi4wdrGNTj\nDjVa+aDRutB0ZAU8XW9SPuQV7evIqVA4DqWNafMWRXgTY8O9x3Z0+9kTUdTx4+/V6Nj4DkM7ncTF\nMWMrND5RyupdZdg7fLPZ5/NWZcu2s3U50nMmkCSN+SrOkYgYR269suV6hJyw10pexLviqEikQ+ln\n1C34GHtF2h4PUYRhe75hbJ3dyKTW69cNoNIo2HixMftHpN18pHTwG+7OXEvbhWUouXQsc2ovQKt3\nQJTb0rJl1qzolMZHVgyDYsWK0a5dO0qXLo1EIqFkyZJ069YtS3PLDsiOJViCIOQGugIFRVFUC4Kw\nHmgJrDR1jC+SpNVqNRqNBnt7e+Lj461Kbllxd5tLftZARvPX6XTExcUhlUpNDhVMmPAKL3cV39TQ\nEBklpXEXHfcfF2LUuDgaNXEkKQHsfYwY8pCgACdqfZV1d6Uowg9D7BjQ6xn29qlv4+qiZ+l8Cfcf\nPKPXwAD86+dgSNtTDOtgHlG3HOFKu2Z3cXOxnptVJhN59tyLratv4+Up4dAxFw4ctafDNBfeRvnh\nYBdOkO99GlXU0KyaiEJu4PZDWw6eT+T8bSkPX7oQFedDQoIfCOBo/5q30b6M7HaRAW1fmVWW1mcK\n5Pe9R9k86Xe1+hCXH7pSZ0oVQEPtZR1R6zzQ6+2wVbzFzuYtLg5ReLnEk9MnntKeGp5GujL+cFF6\nbc6Dk90tSvheomu5F1QNeoxC9u43Wnw6DzKJgg7lbpo1n8xgwOaC5Pe7S6nAN+lup1To2NTvNBtO\nP6bHb/0RBC0/z5RkOkkurQV6Vt4VQ4YMYciQIZneP1viMzTYMAExJGl22wmCoAfsALPcSF8kSRtV\nfLK64jQH5lq6Wq0WlUplUpz8c/R9TrmAsLe3R6EwTR0rKgrmz3di14pn/LJYw4ylxQit9Irl67Q4\nOKY+xssXcGB/CIe3hltk7gtXxCNIPOjeOWPd5qBAPXs2w6kzr+napyx/Hb7HoUVvcbTLmHT3nrbh\n5dt8jBkQZolpp4kB41XkDY6gbMmkOXVsAx3bSIAYEhJjuXhFwd8HvdlwUsr0tX4YDFKcnV/i7xNP\nvjwG6jdSUCREJDDgPq4uepp3iEJueMGQjqaLy0BSBvvWg+U4Nd60JKNEjZRZu31YeKA4qsRcaLR2\nLPlhL8UD3+LlEo+bQ0IGHbJuoUo8zKErOVh7wpc+20N5G+ePm/1lKuS6RrdyL5lyqCnzvt2JxIK1\n1qkhTq1gy5XGHBm13uR9vqvwhNjEA4zcXI22bdNYLWYC2SU/xYjIyEiio6ORSqXY29vj7Oz8edrj\nZkNLWhTFSEEQZpDUnjIB2CuK4gFzxvgiSTplpp21yS3lcUx5cIx9qbVabbL1bAqsdR6pLQDMWUB8\niD69n1IoXwJt+spI1ORj8W/xlC3vRGrWsxE9u4RTp7qSPIFZd1cmqgV+np+HX2dHmuU2Dy2v5+zR\nSDr2dCOoUSCbpl2kasm0Y8yiCN0mBzCo+0OUttZzs8bEStm2tyR/b0xdG1ppKxJaVv2fEjQD8GHN\nsgTQ/ecDES8k/HO+FFf+OmP2XNqPECmf7xIh/uknrt187EzvVb6cD6uOv9djJv3wkrnr31DYT0eb\nquaVqNnb6mhQ9hkNyj4DrvM2zoY9F3Kw7kQwTVc2RqNz4f4brFpeB9B3cwiFct6iWED6VnRKiCJM\n3VmGiZMwqV1n2uO8/25Rq9WfXR3szZs3HD16lKdPnxIdHc3r16/RaDQ4OztTtGhRKlasiL+//6eV\nK86GYiaCIAQD/YDcQDSwURCENqIompxO/0WS9Iew9srT1LE1Gg0qlSo5MczUG/hTrZqNZWrGUIGp\nCwgj7t0T+WuzDxKJlu9aPWfIcAkZ6a5cOKfmwYMCbF9pvqxkaug/MprcuWypWc184rSzE1m/En5f\n/ZZGA6vQsvZxFg3VpPryX7ZVgd7gQq8O5gt5mIMew2MpUeQxIfktozfepW8kX4fG4+9lXi3x0xcK\nTlwsx7XpqYfSNDoJC/b6MHtvEWLjg6hX6TpnR58kT84Ezt20JexJKIfGrMny/F0d1LSu8pgm5Z/j\n26kQY78/zIKd9VhwMp5fm+/i64Lml4RlhNhEG3ZcbczxMeY1AdlwJhdalLRrlzUrOrVe0p9bt/vg\nwYMcP34cuVxO3rx5KVGiBBKJhBcvXnD06FFmzJhBtWrVGDZsWHIWubXxOSzpYzcfcOxmusmcpYFT\noii+ARAEYTMQCvz/JumUghqfIukqI3e0UZREr9en2Zc6K+NnBcaxs2I9G9Gi5ROcnZ35Y52OwKCM\nXyKiCP16q+jdOQonx6xboy9fSdi5ryT7tmUtc7jD9wJVKz2jedvCFGj+mmNLnuHl9s79rdMJjPy1\nMDNGvbBIkltaePlawuGTZTi2y3Rt6PTw8LGEK9dLsmHbabP3bTVEwjclz5DTI/a972MTFLRblJvD\n12vg4/6ckZ1f0K7eIRTyd/dr65Ee9Kp3Emc7y7UH/WGxF3l8nzCk2T0GNb3H/B3+dFjTBR/ny2xs\nf4wgT8uUqQH03lSEogHXKZzT9JagoggjNlZi3ESpRQy8D5tr2KeVbPGJkCdPHho1apSqRd+hQwcA\nVq1aRVxc3Ccj6bSyq62JKiHBVAkJTv578taPOlHeAkYJgqAEEoGagFmSeNnPP/BfiPTkR9VqdXK8\nxtKSnpaAsY48Li4OOzu7TJepHTmiJvyBB/uO6AgMMm1BsWzJKxAdGdDTUiVXMVSvGk7e4KxbnYG5\n9Zw6qKJkKRsKNqvAhv3v1rNjlshwddbStJ71elIDdBmkolKFB+TOZZmktE69o2ha8zo53M0rFbsZ\npuB6WBnmtr+e/J0owsTNvuTq054YfW7OLD/DjQ036dIo8j2C3nzIhui4AEZ/ZznhkrdxNvx1+mtW\n9E9KFpNI4MdGT3i0cjOVixkoN2sgjZdVICbRfGWvDxEVr2TPjQYs7mReede607kwSG1p3TrrZJpa\nByyjkMnnQsmSJbGxsWHZsmVs376d16/flaQZ9cbbtWv3Sdtpfm5J0NQseVEULwOrgHPAlf98vcSc\n8/oiLemU+FRJVx8e40NRkqwkUljrHLRaLVqtNtP9qI0wGKBLlxh699NgZ2faizE+XuDXed6smPfc\nItboqbMG7oQVYe3vz0lZcpUVKBQiC2cK7Pr7BT2HVGLd/rP8PlrNok3l2bj4sVVjoE+eyzh7uQz/\nHHiIMZ6cFdy+K3DvQTH+nm9+LLrlUFvaVTmGu2NSSeOxm660WVAJmcyezdMu8FWp1FtCGgzQZ0Ye\nJrY+gY3ccu1BW830o2LINQoHvJ8YaG+rY1Gvu4xs+ZT2M/ORd3wtOpXfyIT6tzNdntV5XTHK5rlM\nAT/Tm5mIIozcVIXxUxRWCZNmB3e3Xq9HKpVy584ddu/ezcWLF6lSpQpFihTBw8Pj8yS2Zc/sbkRR\nnA5Mz+z+XyRJp7xBPgVJpzxeym5Qtra2yc0msjq+Jc/BGHvWarXIZDJkMlmWEjwWLHiLTg/ftzPd\nchnY9wEh+R2pVinrL29RhK79lfTp8QQXZ8s/qPXrQJlSL2jeNoiAhg4E5nxDaGnr6kO36xdPnZr3\n8fGyzO/e+cc42n5zDVcn86zokxdtePayEJNH/8bLaBsazwrh5pPyDGt/iUFt7qRLQjPXKLCRyuha\ny3Jx+4cv7Th1qxo3F6ddp+3nHs+BSZf459ZDOsyqzOrxtfil4WZalEo9+S4tvIix49jd+lyassKs\n/f48GQAyOS1bKs3aLy2kJwn6uWCsnpk+fTpRUVGsXbuWESNG4OnpSYcOHahatSpubqlLpFoNkuyX\n3W0JfLHu7vSabFjjWEZ1s5iYGLRaLU5OTiiVymxVKgFJ1nN0dDSiKCarmmXl+qhUMG6cDROnmp5c\neT/MwOmThVg6yzIW79wl8QiCI326W+9a5/DUs36lFp3OlbCHvsz9zXokfSdMws27JZg62jKP54XL\n8PRZCBN6Z1yS9iE6jnKhT+2jjFjvTb7+nfH1cSVsy3GGtI1M9/fWaAWmrSzFwu7/WtSabDo9kGaV\nzuLnHp/htuUKvOXGr0eZ1e0y/be2p/7iqqh1ptsl7f4sRfUiZ8mdIzbjjf8DgwFG/1WF8RMVVvO0\nZAd3N7x7x6rVaqpWrcro0aN59OgRvXr1om7duuzcufPTlo5KJJ//YwV8kZZ0Snwqd7darUan06FU\nKtOVy8wMLHEOKa1nc0q/MsKAAc8JzquhQqjpL40eXSJo0/wVfj5ZJ2lVvIRZv+bjtwWvrZrEBdC5\nVyRVq0lo38mR3t1D2LrvDjtWyLG3s2wJVvv+Wpo3fICbq2Xu2x4D1HRvfgNHe/O8FpsPyHgbnZtf\nD7jg7qrl8K9nKJ7PtD7NA2Yp8Pd4Qb1S5kuHpoWzd50Ie16WQ1M2ZbzxfyAI0KZaBHVKbafe2JLk\nmxjCzm5rKeKbfmLZo0gnLjyqza0ZS82a4+qTuZEopLRoYRmNbkjdkv7c7m4j5s2bx5MnT7h06RLe\n3t4sWLCA0NBQHjx4QNWqVQkLC/t0eTjZsE7aEvhiLWkjrE3SxriuwWDA2dnZIu5tS0Oj0RAdndRL\n2dnZ+T2Czsr1efRIZN06D36eafoLY+vmKGKi/Bk72DK/SbcBURTM/4qqla0rCXnlqsjN20WYW/9r\neAAAIABJREFUONWV0mWlHDwuIrPLQUg1H06ft9xx/r0k4dHTwowdZpl76NgpA68jgxnR1bxe2o8j\nFHQaUx4DCib1esi1tTdMJujoOBl/7q3I730uZWbKaaL1rBB6NziNs735CXvuThrOzDjDDw3CqD6/\nPxP+zpfu9m1Wl6VR6ZN4u2RssRuRZEVXZeJkW6vmK2SHmDQkVa2cO3eOsmXLsnfvXlauXEloaCii\nKBIYGMjAgQM/baLs59bttlJ2+RdrSacsvbIGSaesKZbJZMjlcqsV7mf2HAwGQ3Jjd3t7e4s/MO3a\nPaHeN3r8/E17YWg0MGmcI9NHR2Brk/Xf5H64lGOnSnLywDMskVyVHjr31tGm3SucXZI8BvYOIqvW\nOvHHigSadg2hdaML/DI66y/nzoNkdGv/EEcHy9yzfYZKGNjupsmCKxqtQM9JEjbtq4iNXEv4tkM4\n2JlngbcZZUPZvNcpEWS5MqitZ1yJUgUxqtWWTI8hCDC61UPql4miwdiG7L55k309D3zUf/rWC1du\nR1Rh9zDzrOiVxwKR2wo0a2aZWLQRoii+927JDiVYABKJhJUr39XNGwwGJBJJspHSt2/fTzuh/1nS\n/52wBkkbLVNRFD+JBF5mzkGj0RATE4MgCOmWfmX2+hw5ksjVq+4MH+Vk8j5jRz7C1zuObxu8e+nH\nxEq4eceWLbuk/DQxmu86v2HOkkSev8h4QdGym5oWzR7i62Ndgv5reyKxcX782P9jl37bjkr+2pHA\n7mPBlKhjw8vXmX+ktu41EBuXk4G9szLbd9i0XYM60ZOB7UyLRa/fKyVX7SKcvxOMQh7LitFnzSbo\nsCc2nLgcyu99rme8sYkQRfhhaRnGtjmDjTzrHpNSeaK5u2wP3jkcyD+pD0fueL73/+9Xh9K64nHc\nHBJNHlNvEBiz+SsmT7W8FZ2au9vJyfTnzprQ6XTJ749Pqi6WGiTSz/+xAr5YS9oIS5J0Wpbp59DW\nTgvWtp6TjgFdusTS60cN9vamZXQfPyKyfWtRcgdcpthXMuITPElM9EQUpdg7vMHJKQZvnxx4eUvZ\nuFtkxsKcyGQx+PvdpXEdOS0aO+Ln8y4z+a8dGt68DWLsT69IT3I0q9DrYeR4dwb/lIBckboUY1Aw\n7Dus4KehDhSv7cacsTdo3sC86y6KMGiCO8P7v8BGkfXzMRhg5ERXJvQOy7CBxuMIBd/0ceBFZF7G\njX3DhfNv+FenoUFl81zkAE2HONGm6imTErtMxS9bPZBLbelZz3LtLe1tdewed4nFe17y3W+9aVZ8\nM/ObXeHSU3ceR5ZhakvzrOhF+4Oxd9TRoIFDskVpLahUqmxhSQOfRaM7TXzuRYKVkI2usGXxYVlU\nVmAU/IiPj8fGxibV1pfWJGlBEDAYMrYgUsqOmtqeMzMLjHnzItHpoG2H9AnaYIDNm6KZO0tL5Ju8\nePtEUaueB3nzO5A7UIGPrwpHJxFBkAFuH+wbz707NuzZ5ceWfRpmL86JVBqHv+9dvqklZcmqXIwf\n+coibvP0MHVmNA6O9jRtlr5WslwBP89yYv/eePoNKsy6HVdYNVtpclLZolVaZFI7OrQyXdUqPcz/\nLR5bhRMdGqVtRWu0Aj0nSthyqDyNGjxmwtgotDoZP40I4eCCf8w+5t+nbXj6KoRfJpsnn5keEjVS\npmyuyZohJ6zyDu5e9xk1i23n61GVKDKtIKIo0q3GURyVpse9tToJk7dX49dloNNpUav1CIKAVCpF\nKpUikUjecwObi9TETLJDTPpD6PV6YmNjcXR0/Kjd7ifBF1qC9cWStBFZTeLS6/XEx8djMBjSFCX5\n3IliKa3nzMiOmoOYGBg/XsmCxXFpvjRVKoFfpj1mx1Y/bO0cKFMJju9TsWW3FDt7o5sufRe1RAL5\nCujJV8CJvgPBYEjg3l0F+3b7sWy1FFW8D5u2PaBOLQ+cnayTNKZSSVj+RwGW/K422YVZq7aCEqW0\n9OnhQ97KHrRvdpnxg+yQy9NeTGi1AtMWBjFnSpRFiEirhTmLAlg+/m6a816/V0rfaYXw8U3k750v\nCQ6SAyLdOz6ndEgkJQukLlCSFkQRuk4KYkyL49jbWi780HOxN0Hez6lTyrzWmOYg2DeOW4sP0WBc\nCY5eLUter2Vm7T9zdz48veKpXz8H8K7fs16vR6/Xo9FoEEUxmbCN5J3Z90ZcXFy2cXenXEBERESw\ncOFCihcvTsOGDT99E5BslrALIAhCfmBdiq+CgFGiKM41dYwv0z+QApl1RRtFSWJiYpDJZMk1xZY8\nhqlIb3xjfDyj2HN6MGfuPXs+pVDhF5Qp9/Gt8/iRQLtW9wktbc/5Cy6MmeXI6j05OHHAwNBRKuzs\nM3+NJBLIl19P81aOJCa4smhlDFq8KB7qy/Axb9Gap9FhEnoNfE3+Aq8oVdq8x8TDQ2TtJmeW/6Fm\n78kAgivlZP5KDWld5rEzE/Bwj6deLcuQ25ip0fh4RFO/8sdEe/y8DYW/daPv9NJMGJvA/t0QHJS0\nyHn6TMLpM8VZMdK8FpYAM/5UIJPY0KdeeFann4yXUTb8dbo2qwZaLr6dFmRSAzcf2/BdzfMMW9+E\nr6cWI1GTsWWWqJEyc0915s53Tf5OEAQkEglyuRxbW1vs7e3fCz0ZPV7x8fEkJiYmV4ek9RxmRzET\nIwRBQK9PyluQyWQEBASwf/9+Jk2aBGCSB9BSEKXSz/75aE6ieFsUxRKiKJYASgHxgFnZj1+sJZ0V\nMROjpCeAk5NThq6bz0HSlrKezVnNX7umY9cuT/4+FEfKOPDpUwmMGfGGly8KUq6KN79ts8HHL0mz\nd/rI63h5OdKkmWVW/t07hFP9azfKlnejbHlPblzVMWKgL4XK2jBi0DPatbazyIL62XMJR46XYOe+\neDIb8y5eUsLuA/Yc2KdlwuggZi+NZ8ao1zSq/Y70VfESft9QlPXLn1tk3vHxEtZsKsyu+e+0prU6\ngQXrpMxanZNETQ5afveSIQOjsLV9/4Cdu0bQpFoE/l6mJ0wBJKolTF1Zmj/7HbKoS7r5L7moXvwy\nIblMFxPJLP445IJal4Olw08TFfeURoNzE9ivIDsG7aF0UNqx+YlbCxCQ+y2VKnmnO74gCMnqfvBO\n31qv16PT6dBoktzrKS3ttFzk8fHx2SIm/ejRI1QqFQULFgTAy8uLbt260alTp+Tz/KTJZJ+hwYaZ\nqAmEiaJolgRftj+rrMIcAhVFkYSEBGJiYlAoFGbFVj5l4pjRejZqbmfVvW3K3EURWrd5Reu2EXh6\nJm0fGyvQqtlDfujmRpU6fmw8omD0jJz4+CXtE/FUz5G9wcxa6GgRAjqwN5bnz4IZOeFd/DqkiITN\ne10ZPVnK9Ln+lKgIp//NutRom85R1Kn3HP+cWf9da34t5/ApOb362fDjmHwUqWnD2ctJj17vkSry\n531OuVKWsaL7/vSGkOBHlCsaz5toOe1GSPCpUZZFm/MwbKiMK+ffMnqEHFvb98/rwkU9D8ILMbv/\n6zRGThs9pykI8n5G3VLmW+Bp4dpDBy7dr8KS3nctNmZaMBhg8PKyTP7hJjKZiIeLlhNL7jLw+8fU\nnNyeH1cGpOoFiUuUs/hQdRYs8vz4nxnAGLNWKBQolUrs7OxQKpXIZDIMBgNqtTrZ2ja6znW6pHvE\n6DrPLKKiomjWrBkFCxYkJCSEM2fM03M3Wsd37txhzJgxXL6ctCB89OgRAwYMYMyYMQDJFvangiiR\nfvZPBmgJmN2v9Yu1pI0wlaR1Oh0qlQqJRGKS9fzhMawJ4zmkbHmZ1aYdKcc2BatXx/L6lS0/9lcg\nivD7slfMne1L4RKerNlnh5PzxwpLw3rc5JuGjgQFO2d5nlotjBomY+BPCdjZv38sQYBadW2oVgt+\nX+LA911cyOl/g9VLXfH3M/9FcfiYjsdPC/LnXxoslTkukUCr721p9p2ehfOcaNzZAz/vWzx6WpZD\nW8MtcozIt1L2HizJ8vFXKf+9HbfDy1K82APW/xlN8WIGIO3fulefBPp8dxlnB/MWCy8i5Ww5Uol/\npn+sApaokfIi2o5X0XaERUgolDORQrnemrRg+/bnELrWOU0OF+tqpANM2+SGnVKgfb13TTQEAQa1\necM3oSeoP7Ai+4bk48hPJ/B2TUjeZvSmEAoWfEnJkr5ZnoOxra7RTQ4kSw2r1Wq0Wi3Dhw/n+PHj\n2Nvbs3z5cipVqkS+fPnMfv/07duXevXqsWnTpuT3njkwWscVK1bk5s2bjBs3jmLFinHx4kVy587N\n4MGD39vukyEbW9KCICiABsBQs/fNgMCyR11RJmAwGNBqtckZhy4uLqluZ7Se1Wp1slymuTe98UZ3\nds46GaUGYwwLwMbGxqKa4KbMPSEBAgLimDRNRZ68Ujq2fYUq3ovhU5SUDk1duOHvbREsnm7L4TNg\nm/WOgYwaFs7F8x5s/tslw5e8Kg6mjX/D3l3eNKx/kdlT3Ux2wxoMULSCgm495bTrZFlRipSIixWo\nV0tFVJQPUokON9fblCgcRavmXlQqK2JnhtRonErCoycKOv+o4ekzb6QyOY0bPmXQACUe7hkvUrbt\nSGDkqBw82n7qvTaTGSE2XkbJ73OTqJbh5xHO2zgnVGpnNFp31Bo3DKIcW5to7GyjcFCqeB3lhVYn\nx9/jIs3Kv6BzzfiP+lNDknBJl4V1ebJqK7YK61pjGq0En7YNWTXmGnVDU8+E1+oEekz1YfOR/PzS\nehOdq70iSmVD8IAeHDkKISHWIwdRFJNj0FqtlmvXrtGvXz8KFizIyZMniYuL48iRIxQuXNik8aKj\noylRogT371umdejZs2f5+eef2bRpE4MGDWL69FSbPVk9o0sQBFF1wnS5WEvh2IVrHL/4Lmdi8oqN\niKL40fkKgtAI6CmKYh1zj/HFk7TBYCA6OhpXV9ePttFqtahUKmQyGXZ2dple+WW0EMgKDAYDcXFx\n6HS6dJPXMgtT5t6zZwT/ntWSJ+8bdu0oQJ0mUfQc4k1aXnaNGpp/9Zqxk/TUbZD1DM+I51Cvhi1r\ntmgJzmv68/74kUiPdnEgRrF7k5wcnhkT389zYli7yZ8Dx63TZtCIe3cNNG/kwK4jOgx6gdMn1Bw9\n+JbrV2yIjPTDzu4xATkfUf9rJU3rOyMIInfuwYl/XnPluoYnz+2IjnEnIcEHvd4WpfItKpUHA/qG\n072rAVOl2fV6KFFayqQe4XRqmHE7RlGEYxftGDxPwa3wUAwGOU2rnSM4l4bcvhDkJ+DlrsHTVYOz\ng/ajBdX9J0o2HbBh62F7bofnQyaLIo/PZTpVi6Z5xWic7dT4danLmNa36WHBuui08OOvnhy5XpBL\nq29luO3fpx1pO7YkxQL+IcBdzhOC2P131q3o9GAwGEhISEiOQYuiSL169Thx4gQAT58+xcPDw+RM\n6kuXLtG9e3dCQkK4fPkypUqVYs6cOdjZma41rtPpkMlkbNq0iYULF9KiRQsqVqzIuHHjcHV1ZerU\nqR92wPokJB138i9rHyZDOFT8Ni2SXgfsEUVxZSq7pYsvnqRFUeTt27fv3TQpk64s0WxCr9cTExOT\n6kIgs0hZm61QKNBoNBYd34iMSPrBA5GiRQ3IFa9xddMzfq4XOQPTDwWMH3CNl88c2bTDMp6FRrUf\nUqCQCxN/cTd7X50Oxv8Uyf49rkyfcJ9mjdO2jlUqCUXKe/Hrb4mULW/dmss61Z9QobIrw8Z8/Jtq\nNHD9isCh/W/495SWJ4+9EQQDTk6RePloCAySka+gPQVCHMgZIOLmLtKs3l3KlLDn56nm3ctTp79h\n53Y3bm24mq6HIipWzrhlEtbtL4hBdOTbb56xc7+Czg3fMLqb6b2WU8JggMt3HFn7t4w9J114HJEX\nmfQNgiAlYvVWFBZQF0sPcQly/Nt9y965/1ImxLSSs7excur2C+b6/XxcvKghMNC6/PMhSRsMBho0\naMCxY8cyNd65c+eoUKECp06dokyZMvTr1w8nJyfGjx9v9lgbNmwgMDCQMmXKJH/XrVs3vvrqK1q3\nbp1S1OWTkHTs6W3WPkyGcKzQ6COSFgTBHngIBIqiaHYW5BcfkzbCWMaQGcGPjGDpmLQx9myszRYE\nAa01aozIOGZfrdor9AYPOv8gp0lrrwxdzQ/vazlzPA/b96qxxBrv713RREQE8cdfmbvGMhmMn+5G\ntVpqhg4KZuvO66xY5JqqF6Dbj68pVFhC2fKW94ikxJGD8bx5HUi/oamfk0IBJUqLlChtXFiKJL3n\nPlykJJHY2TMJRDzNx9jNrzHnmsfFCaxYmZcdM8+l+ruKIhz4145hC22597gcBfLeZ97UBGp9FcOy\n1QmIeg9+6hRm8vE+hEQCJQrEUqIATO/3lsjoJwQ3DMXT9S2+7eozuf1xutaOslr5a8fZHhTJ+8Bk\nggZwddSS2ycOn8DHBAamn9FtCaRWfqVUZj4M4+/vj7+/fzKxNmvWjKlTp5o1xr///kvu3Ln57rvv\nPvrfkiVLgCQv5SdtrgHZsk4aQBRFFeCR2f2/WJJOWYIF76xnvV5vccEPS5Vgfahs5uDgkKw29jlk\nRzdtiiM2zo5VuwRyeGfcwF0UYXiPB7T63hb/nFkvudJqYNwIGwaPSERpl7X4cLVaNuw4CN3b+VGy\nspZta7UEBb77/70wOPVPCfYczHzJlSkQRRgxTEfPvipsbbNe6yqKMGJgFD17RGNvb97j3LtvBCXy\nR1Gx6PsklaiWMGS+nA0HCiNIbGnROIKN3cLwdNf95/8CU2YHsWLsjQwlR81B94kSiuYL5/DvL/hr\nvz0DplZl8oYXrB9yjXJmiqtkhBdvbdh7vgbnVx43a7/wZ7bs+7cI165ZdDomI6s10t7e3uTMmZM7\nd+6QL18+Dhw4QKFChcwa4969e+zYsYNcuXKRL18+/P39kxcOWq0WQRBYvXo1jRs3JiQkJNNzNRcm\nZFf/V+KLJWkjjOQWExPzHvFZ61iZHTs9ZTNr1mGnNXZiIvTqJdJ3lEAObxMzwBc/QK9zpd9gyyyA\nRgwJJ4e3Ow2/tYxwg7sHbNjpwuxpUdRo4MXQfjfo0SVpMdGuWzxNm0fg7WNducUVS18hlbrSqr1l\n+g1vXv8GndaVXj3MI7FHjwROnirGtbXv3KaiCIu32DDy11Lk9I/m1xkqqlc2ZmO/y/ruMyyaYH8J\n31SxHHE+eCrnwD+hXPgrqe/nt7VUNKx2g2nLHKg9uiH5/f9l68jH+LhZJtu7xXQfqpe5QbB/QsYb\np0DXqb40+/YlXl45LDKPjJCaJGhWa6TnzZtHmzZt0Gg0BAcHs2LFCrP2b9WqFcuXL+fixYtcuHAB\nW1tbpFIparWasLAwoqOj6dSpE4GBgRkPZklk4+zurOCLJumUoiT29vZZjj2nBeNDlBmSTmk929ra\nfrZ+1B/OvV+/CLz8DHxV27TEmJhoWLfck1+XJ6aZUGYO7ofpObCvABt3fZx8lBVIJDBguAtVa6jp\n3yMPO/feo30bW16/DWTwcCtnEqth4XxPJs+0TC8AnQ7mTLdh4rhYZDLzLlLHLq9pUetFsnDJxds2\nNBvuR6LWm/nTXlG/VurX4ulzKX8fLMnZP09nef4p0WSgIy3q3iTA951mtlwmMrJHLL1aX6D3RFfy\ndytP4woHWNLnVZayvm89sufC3crc2nDYrP0u3bHn4u18rN/5+dyqltDtLlasGGfPns30/ocOHaJz\n585ERkby5MkTwsPDiY2Nxc3NjTJlyuDhkWnPbpbwpVrSX+bSgyTSiYmJSe7zbO2avcwQqzFpKzEx\nEUdHxzRLq1IuAiyN1I53546BtWvdGfWLj8njDOt+hQqhryhTLuvrPlGE7h1e0azlK3IFWOeFWKqs\nnF1H5WjJwYBhhWnTTmWRUrH0MG70I3z9Yqla3TKLxTk/P8LVVUvjhuZdo6PHNDx7npeZ/V7xNlZO\n9V5OVP+hCs0aS7h6LCJNggZo1TWWJtWvkSeneapk6WHXcTnPXhbk58Gp59S4Oun4c/pbTq+5yM2I\nvPi2bcSMza5pyqxmhG+nBNG+/iW83U1vogHQfVpOunaLxEqVlqkiNUv6c0uCDhw4kLi4OCZMmED+\n/Plp2LAhbdq0oW7dunh4eHy2joAiwmf/WANfrCUtkUiSs6GNWd7WhLnKZmq1moSEhM9qPacGg0Gk\nWbMX1G8uxcvXNJfeyYORPAkPYuUaPZaI5y5f8gJ1ogf9hlqXNR0dRfLlj+Zh+FuWL3UjIf4OQ0f4\nWyX/JDpKYPeO/KzaZJkEwHgVbFqTkz9XmSYOYoQoQv+BUn7qcJWxS2Us21aRCmUec/5QOJ7u6WdT\nHzim5/HTghxdbJ5CVXowGKD7xGDG9rqNvTJ96zhfoJpTa56z53g0vSaEMn9nJEenXCCXl+ku8L3n\nnYh4G8KUH8zLjj50zpGHEf6MHPlpk6GyI0kXLVqUSZMmsXr1ajw9PcmZMydKpRJnZ2fs7OwoX778\nZ+mCJUq+TDr7Ms/qPzAS56fo92zqMYwueFEUzVI2S3kulkZKRbPFi1/z8pWSLn1Ny3DWaODnUTqG\njdLg6Jh1Uo2JEVg015fZi3UWcZunh1cvRXZszcO81QoECQzr5svRI89Y95cfzs6WvV/69AyjVDl3\n8hUwX0IyNYwYeJdCBR0pU8q8R3jRkih0Wl+m/yHH2Rm2/vGEkkUzdh0bDNB7iBOju13D0d5yXa7G\nLZFip5TSvYXp8e26leO5u+c2A6Y5U6R3U37ptIuuddNuyWmEKELnOcX5qcMV7GxNd5eLIvSekYch\nQ+Kxtf2EZnQqUKlUn71N5YgRI1i9ejVKpZILFy5w6tQpVCoViYmJREVFceHChSxloGcWhi/U3f1F\nk7QRn4KkIX13dFatZ2ueg3Fur1+rGTXKkeHTBGQmEuS04dfw9XekSXPLvLx6drpP8dKulAu1flyr\nd+d7lK+ag6D8/gD88bcnU4apqVZRYPrMGGp+bZmX4b27Bq5eLszOw5Yht5cRcOp4CIf2vgRMJ5u7\nYQI/zyiCQq5h/LA3tGuhN9kKnzZXhdLGiV4tojI36VQQq5Ixf105tsy7brb3QiqFOT9F881XV2k7\ntA4bTp5j55hwbNKprZ63wxVB4siP390261gbD7qgSnSgd59Pb8FmR0s6f/78TJgwgW+//ZbixYt/\n1rm8h2zijbQ0vmiS/tSWdFowt6vWp4RRBF+j0TBkqIo8BVSUreRn0r4P7mg4fSwPK9ZouHxR4PrV\nN9y49oaH4VrevLYhNtYJjdoTgyjF3eMuVaoKtPg+kOA8hlSfp1PHVdy5lZ89x0SsraNz4kgsjx/l\nY/rydy88hQ2MmeXPwV2xDO7vSZWqt5k5L4Cs/lw/dI2gaQtnPDwtI0bTt/sdvq7pQK5cpsW21WqB\nAUNesHtPadxdY/h3/1PslKZf3+gYKYtWhLB99kWLqrC1GSGlRMFHVCqZ+fh2rdBEru+4QsNe/uTu\nGMSBSacoFBD/0XZanYTxayqz9KebSKWmn7teLzB0QUEmTpZk+T6wBFQqFZ6elvHGZBXZiqABg5AN\nfiAr4Ism6ZT4HO5uS8aeLb3QSJlVLggCd+/asHuXkpW7MjahExJgxbx7bFubG1G0o0vbWOzsonBy\nFcnh405gARuqBDkQEORIDp+k8z11OJATByLZ3kxAr5OTw+s2VavJ+a51LnIHiej1MLgv9B4Yg7OL\ndS0FvR5GDtbTqa8W+1QOVaO+I8VKiwzu4k21im9Zs9EF/5yZ+9127YghKionfYdY5gVy4VwiDx8U\nYNOa1xjFTNLD2vVxjJ/kTQ5vP6RSHTvXRJhF0ADf94yiQjENlUqY14ghPdwJl3P8QihXtp7P8lju\nLjpOrH7GxF8dqTCwCYO/3c2oVu+roA1Y5oaPZzSNqqbddjI1LN7iio1SpFUry5TMmQtRFN9Les0O\nlnR2hZhNS7AEQXABlgGFSLI+OomiaHJix/8Lkv4cMWlrWM+WOocPFc1iY1W0ah3Ldx0luHmkLb35\n/InIjDGXuHE5BIXSHgcnFav/lmOrtAPSf4k1/d6Fpt8nxbkjnsKxfYGcOhTFXxtliAYDMnkktrZK\nWrWz/stwxuRw7OzdadQybcvWw0tg2VZfFk1/ToPaSvoPfky7juZZMDodTBitYNBPGmxssh6jE0UY\n1vctPbpF4eSY/qN77x606xxHTKwfP00SWDbvKU3qR5M7l3lSm/9eFLl8rRi3t57KytQ/QqMBbnRo\ncgM/L/MyrNOCIMConrHUrXyZJj9WZds/tzky5R4OSi3RKgWrDtbi4IJ/zBozUS1hwopiLP9dyDae\n1OwQk86uELOvJT0H2C2KYjNBEGSAWYXu2XPpYSF8qDpmbYiimKWe1OnBUudg7EUtlUqTG3bMmqVC\nq4M23T4maFGEk4ejaVvvKp2baJErPRk8wx5NoguTFtpjmwnu8faD7zq6MfuPILaecmD0LDsS4nMS\nF2dPgxrh3L1tHQlUgMg3In+tD2bEL54ZvnilUug93IeJCyTMm+1Ds0YPeWVGy+QZ057i5CzS8FvL\nJNGs++Mlep0LfX5Im6ATEgQ6dnlJnYbehFZzZdcJJQqFmpcRQUwdZd7xRBE69bFhYNvLeLpa7jdZ\nuUNGdFwAk/tlnOxlLkoXTuTWrpu4e7iQu1Mdjl21p/XPOShT6B4l85snvjJ2mSe5AqL5+uusN4nJ\nLLJjTDq7QhSEz/75EIIgOAOVRVFcDiCKok4URbPcOf9vLGljo3JrHyM2NqnW09Kx56x6A1I2FUmp\naPbsmcicue7MXCF9L96oUcPqxffZscEWUFKjqT91WzpiY+vIsO8vUa2OC/kLWaYD0MyxYdRv7kKn\nvt4sn5uD77+1o1CRG8xalA9nFwtnWXe5R+lQT/IXymnyPsXLKvlzr5JfRnlQq6o9lateZ9qMQOzs\n055bbKzAujVBLF2ts4gVptHAgplOzPw5deESUYSly6OZMSuA4HywaS94+bij18PE4Rribta7AAAg\nAElEQVRGDYzE3oz2lwAzF6mQ4MqwjpnX5/4Qao2EwbOLMn/EPWwU1vFu2Sv17Fz0il/Xx1N/XBMM\nehturt9v1hiRMQqWbivB4SOft8dQatrd/7OkU0c2jUkHAq8EQVgBFAPOA31FUfw4cSINfNGWtBHW\ndneLooherycxMdGi1rOlYLSeBUHA2dn5PcnR5t89p3KNSPIWTPpOFGHZnDCaVIrn6H4FHQbnYO42\nb5p09MZWCXs2PCA+zpsfR1mGoFctDEOvc6NLf28UNtBjsDe/77JFZuvB15UkjP/pPlrLeET597SK\n+2H5GTzBdII2wt4RxszOxdItNjx/6UGlsnImj39KWn1P+vQIo3jJlxQpZpn7YNKo+/j5xlK39vsE\nLYrw9z4tZSsmsuBXPybNEfhtgxde/9Ghmf/LA5wcoGMr8xS6YuMkzF1SkOVjwyyaMNV9kpQAn2ia\n1Tb5HZVp9Gihwt/rDgqFiup9fIh4bXpNX58ZnpQv/4x8+fSfTTs/NfyPpNOGKEg++ycVyICSwEJR\nFEsCKmCYOef1RVvSKd3d1nrI9Ho9cXFxiKKIQqHA1kqyVZk5h5TWc2pNRdavj+XOHUfWzE966O/e\nTGREr2cgODFkppI8hYPf2z4uBrYud2LCPLnJ/YrTQ+RrAxt+92bKr/L3Sr5c3QXGzwvg/m0d039y\n46uyifQeEEPLtjkybZXq9TC0r5q2PeU4OGVe+9g3p8CcPwK4cVnDzyPd2PKXnt79omjXwT15bndu\n67h80XIlV29ei+zdlZcdW15hTBaLjxeYOfsN6zZ6I5E60qKdjnZdHd67jrExsPnPXGxe9djs69a+\nVxSlC+n4qrTlksWevFCw7XAo/6y7aLEx08OB01JevAni0pHHjJoip2CrSvzS5wSdG6bvur//VMme\nU0U5f0GDXq9Ho0laJUokEqRSKVKpFIlE8knCaP9zd5sOw2dIHDv9z1lO/5uuxOoT4IkoisaNNmEm\nSX+x/aQhiUB1Oh1arZaEhAScnLLemckIURRJTEwkMTERpVKZvNrOqvh9WlCpVEilUpMXAVqtFpVK\nhVwux87O7qMXSlwcBAaq6D8OyoTaM37gFS7+m4+6LRJo3MGb1HQBRnc5j7+/K2Pn+FvilOjS+Cq5\n87gxbFr64504qGLB5HikkiimzHakTDnzk8umjgvn2GF3ft/la7EyIlFMmtv8SfGIYhwTJkupXsue\nr6s+pUpNFwaPsEzJVbtmt/H2cOS3JQoePpQyaNhTLl0uTs6ACLr3d6NyNUWqJNzz+5s4ypVsXG7e\nYuHSNWjYJphbW06Swy11QjMYIEEtzVAlLCVKtHSjVGE5S8aZl2GdGYgiBH6dk95dtPzQKWmOB49J\n6drfl6J5LrNrRjS2Nqm7/6v3CiZ/CVfmL/D8z1hisrdMr0+yrA0Gw3uELZVKrULaxtaUxgzvunXr\ncvTo0WzlqTMBn6Sf9KM71619mAyRK1+h1PpJHwO6iKJ4RxCEsYBSFMWhpo75RVvSRljaktbpdKhU\nKgRBSI49JyYmJtccf06Iokh8fDxarRY7O7s0m4p06fqMwLwQFyuh2VdqfAPcmPanE26eqYuSnNwb\nwevnAcz7wzILnV2bnvHmVU5mr86YyCrVsKfCV/Zs+l3gxy62lKt4h1/m50Fm4t378oXIlo3BzPlD\nYdE6X0GAyjXtqVjdnq1rZAwdJMVG8ZqExGC69LRMDsT1qxru3g6hbYunVKgSw+vX+an4lYE/d0DO\ngLT7Gd++ruHGlQKcPxRu1vHUaoGWXRwJLXaPict0PIoQePXWhrexSlTxjmh0Lmg0Lmi0TgiCAaVt\nBHlz3aBzY4Fva2hxSkONbOshOc9e5efYsCtmzSezmLFCRCqzp0eHN8nf1aii58KhZ7Tq5kPuJsFs\nn36FsoXfj6WcvurAtfvBbNn3jgQFQUAQBCQSSbI3KiVpazQaDAbDR5a2JfoFpKYyaO0+BP+tyKYx\naYA+wJ+CICiAMKCjOTt/0Za0wWBAq9UmN7JwcTFN6jItpLSejQRofIDUajVardZqrihjPXN6cntG\n61kmk2FnZ5fmw3zmjIbatQVcPcKIfutLh0E2lK2WNvkmJkC/JhEMnKCg6tdZP794FbSoHsWQyQoq\nfGWe5yHylciw7k+Jj01k5QYP/HJm/ML6tu59AvN5MGyqaSItmUW8Cpp/FYetUkO8ygWl8hk5cz3l\n63qefF3fCx9f04hbp4NXLySEP9AxuHc8Wp0D9vaJtGinp2V7Z5QZOBJEERp9Fc53DQyMGmjaMW/f\nlTFswmv+uVAGUJAn8DaeHnpyeIr4ekvw95WRy19BDk8Rdzcdbi56ZDKRK9cVbNyq5sBRW55HBODo\ncJ/SIQ/4sZWSSsVVyGUiOp1AzrqFmdj3GR2bWM59nhYSEiUE1CzKinkRVKv08cJZFGHhcglT5wbS\ntu5x5g5IQBCSvi/6fTFat7djyFDz3hVGWV0jcev1egRBSCZto6VtjrUtiiIqlQp7e/tkQ6NevXoc\nP34822j9m4hPYkk/uGuekpw1EJg3/0eWdFbx/4KkDQYD0dHRyQ03MgOj9SyRSLCzs/vI3aTRaFCr\n1VZL6kiPpI1lX2q1OsOWnDodeHnFEZ+gpHz1V7QfGIBNBh70KX3OoZC7MmOF+QlXqaF/+8vIZG5M\nWZIrU/sbDLDk5+fs2eJI/6HPaNk2bYtyz463TBrtwrqDTpkqFzMHs8be5MoFJxb9lROdFu5c13P6\n4Asu/ZtAxBMfBEGDh+c9ylSQ0OjbYBIS4OK5Z9y4+panT6REvXUkMTEHarU7NjaxCBIVGrUbk2bH\nU6V66i7t1LB2xXP+WOLAlaMv0tU/j08QWPBbPCvWuqCK9ye0UgQnjnnx55InVCpvvlcoIVHg2Ek5\nG7Ym8s95N2JiPcjhfhUnJcSr3bm67f4nqTduOxTCnvtz4K/0G2/cvS+lWSdn5MJrji58wvHLdgyY\nV4x7YfYme2nSgpG0UxI3mBfXNpK0ceFvJOkTJ05kbXKfHp+EpMPu3bP2YTJEcJ48Fifp/xfubsi8\nEEhKAvzQerbUMUxBWi57nU5HXFwcUqkUZ2fnDF1hI0a+QsSG0Yvk5M4XkOFx/z38god3g1i9zzIe\ngjNHI7l3K5hVezK/mJFIoMdQH8p9lcDEgV7s33OPRb/n+SiZTaOBSaNt6fOTYHWCfvPKwIGduZm5\n2gZBALkCCpWQUqhEUha8KMLzx3b8ezyIs8fe0rdHPDKZFndPOT4BflSua09gPhd8c8nw9AJwok2N\nBMb9HEfVGqYnIybEw+I5rvw253maBH32gpSfJkdy625p/Pyf0X+oHfUbJNKxdSQVyqipVD5z97HS\nVqR2DQ21a0iAKF6/iWPtX85MnR2MVJrIoOlhTBsoQSaz3nPy9IWc3cdKc3R7eIbb5g3Sc25/JP1H\nyinQshI2cgMzZ5Nlggbes6KNLnIjYRsMBtRqdXJcOyVx/5dZyNkKqdUpfwn4okn6QzETc7tIpbSe\nMyJAaz9cH9Z6m7N4MOL2bT2LFrkwZoktvrky/unVCbB8uoG+oww4WaB/hjoRpg7X0X2QFEcLjFei\nnJLfdysZ2dOTWqFRLPnDjvwF3zH1TwPu4e3nQY1vTGu5mRWM+OEK5ap6kDtP6t4BQQDfXNC4jRuN\n27hlON4vI67g6+9IjTrmzX14n5sULmhHzSrvW8KqeAmTZkazaYcfOr0Ldb+xZcaiBHx8k9y6Z04l\ncOtWAS4ceYo5TTvSg4e7jk3b4/mm7h26dZbTu38wa2sq+GXQbVp/Yx2i/raflHq17hOU2zQ3v1wO\n86fpgVccPWNHixZpK+5lFR/GqdOLaxut7JTPtF6v/188Oh0YxGwbk84SvmiSNsJcAs0MAX6qTltg\n3uLBCFGExk3eUKORDN9cplnFMwafJ29BF2p8Yxk395i+l/HP7Uadpl4WGQ/A0Qlmr87JmsWvaNdM\nSYeu4fTsl5Owe3qOHynAb1utrxZ17mQ0Tx/lZcpSy4Q6Xr8wcOpgMKu3m3c/3bml5cLZgpzdH578\nnSjCzEXxzF2an1wBSsZPtaNaTT0SiQvGaJZeDwP76Bj642NcLSges/1vDU+f52X7ptfY2xs4tt/A\n5m06Bo8vyvhfH7NhRixF81tOyez4ORlhj4uybc1Ds/aLjZOw+4Av27aLn1T+UxAEZDJZsm5Byri2\nTqdLdpEnJiZy7Nj/sXfe4U2VbRj/nSTNbpPuDYWy9xCUjYgiUwXEwRDZKBuZwseQjTJFcIGAgANF\nEHCiKIqbvfcuHXQ3O+d8f9SUAh1Jm0IF7uvqpV6e8SY5572feT8/YzQai13z4nQ6eeCBB4iKiuLL\nL78s9mcoTZBKPqp+R3BPkDS4P4+5KASY+/olBZcnbTab8yxcKwyz51wjPVNOlwHhbh3/xw/xXDgd\nw7pvvUM8f/+axqG9FVm11fva3IIA3QcF06CZjclDwvjx+zOkpWro2M2PsMj889XegCjCnAmp9HzJ\nD62XaganDNnPI239KVvOfa1wSYJXBl5mQE+RsJBsL/Ln3SIDX9EjVwSzZIWdxk3zLoaaOe0CBl9/\nBr7ovefXZhMYPSmUaZMT0OlcES3o8iR0bJfCvIUaWr1YiTpV/+aTBQIBhuKRtSTBC6+GMLz/BXz1\nnlXWj5suUKv2VR58sGQLCwtD7hA5ZO9FVqsVuVzO999/z/bt20lMTKRTp040bdqUpk2b0qhRI4+c\nkMWLF1OtWrUcZcS7CeJdqs11d36qf5H74S2MRF2tSxkZGajVavR6vcehpZIkaVEUc3q+/fz8UKlU\nbr+cFy6IzJ3jy9DXgt1Sj7KYYdV8ieGTsz3V4sJmhZljzfQfZcM/sOSs3UrVlazeHkhmVhBJiZVo\n0KTkh3W8v/gkKo2Kjs95J0z6x0/JJMaVZ+wUz4Z5rF95BYctkPHDRa5cldO8k4WeQ2Lp3V/Fjl+V\nNG6a9w8ffxW+2FiJlW9avOpFjpiYQkSYmW6db72oUgmTxsn5/eeraA0hVGxbj+GzJOyOoi9g4RqQ\nJCPDBngWqj9/UcG27yqwbJl3etq9DVfb17x58/jss8/o1KkTPXv25PLly0ybNs2ja126dInt27fT\nr1+/UqOg5k2IkuyO/5UE7mqSzo2CSNrhcJCWlobT6cRgMHhEgLmvXxJwtX2ZzWYEQfBYcjQ7zB3P\nQ63TKFvJPVnEBWP+oVK1LB5p7x0vetqoA4RH2WnXteQ3QrsNriUaaPVEGv8b7sPCqUcpqf0oMx02\nrw9n7Owgr/RfO52weGoGL402o/WgM81sgneXBrBg+jVeGpdOw8fKE1sliJ277fQZoC1wbf16nafD\n4+eoXsV7Pf7nL8rY9m1d3ltOgcQfFCiy5n0Fmz+JZ+feWMo8UoWNnklsA2CyyJjzbl2WzknxuOhr\n8BgF3bpdJfLOOtFuISsri5CQEJ5++mkWL17MN99849G+M3LkSObPn3/X5rUlhDv+VxK468PducPc\nec17drd1yd37eBO5x13qdDqsVqvHxsDy5alcjtMwcqF7eeDsMHc51t1Uze2wQ/I1SIqXOH86maq1\nAigbW/gIv72/p7P/rwqs3KK9Lfm+iYP2Ub1+ED2Gl6N1ZyfzRwXSs+0xlqyrRECgdzenycP2Ub1e\nAFVqxXjleh8sOY5Or6Nrd8+Mo/FDjxIUEMDgsSGUjVGzabuJmHIGCuug3LwphcT4GOZ/drXQYz1B\ntz4Wnu58gXIx7hmTNaqL7PxGZNNmJ4MnN+TTr/9m3VzJ7Srw3hMlqlRMoFUzz5TVfv5NwYkzEWzZ\nLgAFt2vdCXhTEnTr1q2EhIRQt25ddu7c6aUVli7creHuu56kXbiZRHMLf3iSey4MnlaQ53cNq9WK\n2WxGrVajVqtxODzXgU5IkJj4qobhs5U3aDrnh7iLIu/OUlI29iJj+mWQnqrGYjJitwVgt/vio8xE\nrU1Dq7OSek2J0ykjOPQETR7xpcPTFQi7yRux2WD66CxeHKYmILhk5FJzY9d317h0oTwL38gOPYdF\ny5m7PoqVc0V6tc1k9FQLD7fzTqX30YNmTh6uzMrt3gmpZ2bA9k/CeWutZ8VL2zZl8ufu+hgMicxb\n5ODhR9wrm7dYYOYUX+ZPj0er8R5Br/3YTGpaDFMnpeIJ8QsCdH5SonGjRLr1KEel9hZ+XBVP2YiC\nn/vTF3zY8dsD7P7qnEfrFEUYMcnIxIlZaLU6bF4a4lKSyMjIKLIOw+7du9myZQvbt2/HYrGQnp5O\nr169WLNmjZdXeefg5fZkr0EQhHNAOtltE3ZJkhp6cv49R9Ku3LPNZiu293zz9aH4JC2KIllZWYii\neMNIyaJ46l2fjqPWg3Kq1M5fNESS4PA/GXy4+Bjxl2qh0UkER+kIiQgmvIwfYVFa/IMFDP4gVxgB\nY855CVck/txZnr9/TmbzBjOCYCE04gwPtw2mzRNlWPzaAUIjAuj0bOEtR8WFzQqLpjnoMUyNJpc9\noPCBAZPK8NdP6bwxVc6O7QeZurCmW0ZLfhBFmDIsjqf7GDD4e8f4eG3EHuo0MFKjtnsRj7QUgRED\njnDsUD0aPnSNt1fJUCjcNzRHvHSGiuUNdO7gvRGuZovA1DllWfR6CuoiFtWHhTr58WsnU2ZAva71\nmDnsDwY9m//79NQwLc91PkN0pGef44MNciTkvPSSAVF0lMr+5LzGVBbVk541axazZs0C4KeffuL1\n11+/qwgawFl6PWkJaClJUnJRTr7rSTo3uTkcDsxms9e959z3KiokScJms2EymXK85+Jcb82adI4c\n9eP1j/MuaLLb4Mu1p9jxBYhOP6IqBpGalMmCjwPR6gsnVUGA0EiBjt2D6dg9GEmCy+f8+H2HyI7t\n6Xy4woHTWYd+I+JvS5h75pj9hEYF0PTxvCuYG7Two2INiddHB/Lco+dY8EEk0TFFY+oP3jyFTO7L\n0308K+7KD0f3ZXHqaGU2/1j4sU4nLJp1hi8+LUdgSDD+/om8vUruUS523z8W/vq9Kr9/f6noi84D\n/YanULGCgraPFe8Hl8thxhQ5bVrH0//l+mzacZAtyxy3zJ/+6CsZSanlmD7hikfXN1sEZi+OZs1a\nCZks2+gqjcgr3O2tIUGl0SgpLkqrJ/0viry4Umt6eBMu0QCbzYZWqy1S5bY7KGpeWhRFMjMzsVgs\n+Pr6otFobnmJPLl2YqLE8BFKBryquUXyMyle5PUxf/JSh1R+3wGd+gQzYqE/5476MmiyqshtRIIA\nUeUEuvYLZ8qKyihVSTzYKon17yno9fhRThy2FO3CbuDYIRP7/qzI0BnlCjzOGCgwfWUMjR7VM6ir\nnU9WedZPC5CeBp+vDWPcnACvzFkWRZg1Jo4XB6XhX4ht9ON3qbR5KJldO/2ZtEhNcqKRBW96ppDl\ndMLQQRZGDD5PWIj3isX2HpD49bfavLfce3Z/syYSv/+UTIYtktjHy3PwxPUv3O4QGDW3IjMmXkWt\n8uydmzpPRoUKyTzySLa7740U1e2At2ZJt2jRgi1btnhhRaULd7qyu4Dqbgn4XhCEvwVB6O/p57rr\nPWmbzUZmZiYAKpXKa+HtvFAUkrbZbGRlZaFSqdDr9fluFp5cu3OXOGo0kFOz4fUw95F/0vjgjZMk\nJ1ahYq0AXp6jJTQqm9QWjdpP7YcCqNckyKO154dFE/8hNNKf/hPL4HTA5g9ExvQVKVdxL/9bWJuA\nIO8ZSKIIU4fF06G7Id8JXrkhk8EzgyOo28TC4lcNfLXpINOXVCPazSKnVwfvo3bDQKrVKVxS1R18\n+NZJfHx0vDAw/7VfvSIxrO8pEuPL0WsYtHnKyLjee3iwkS8PNPRsEMTMqefRawMZNrC4K78OUYSe\ng1S8POgSYaHeVX0yGkS2bYKFS+207N2Akb12M2mQjFFzRUKCrDzzpGeGxpWrCj7aVJ7ffy/9LUiS\nJN3gTGRmZpbYbIC7AaVYzKSJJElxgiAEA98JgnBMkqRd7p5815O00+lEq9XidDpvS2+gu/cQRRGT\nyYTD4UCv1+fo+xYX77+fxrHjvsz/KJtwszLgjbF/c+lMLE3aR9C8kwa19rrH+cPnp8lKj2DQJO+I\nfvzzSxInDpZn3nojgpCdE+7SP5w2z8AH84N4sb2Fpo+eZcT/quPjBXtpxdyjKFVGOvTwTMWsUi01\nCz5R89FyC4O6Oqhc8yBTF9bBrwDO+2d3GudOV+SDYuiO50ZmOmxeF8rSVWKebVJWK0wfd4Kfd1Sm\nWZtg5n5gRK2Bv3Ylc/FsLGvW2/GkOOvSRYkvNlbhq40XvDqyc+rcdFSqKIa/XDLREkGAUcPktGoZ\nR8++tfnih4ucvViFrz+54HEqZfAYOU8+GU9s7PXn5b/iSRenuvtegPMOhLv3/LmLPX8WPPBEkqS4\nf/+ZKAjCJqAhcJ+kXXARtMViuUH7uiTg7ovu8p6VSiUGg8Gt89zxpOPjJUa/omboDAVKFWz64BTb\n1wcQWz2A8cv90OhvzGelJDrZ+XkwY9/QoPSCeqbFBG/PsNFzhBY//xs/k94PhrxWnivnHbz9mi/P\nPHyN7oOy6NyjTJFz1nGXnXzzRVkmLS+4Fzg/qDTwwqgyPPGCxKrXg3iutZlmrc8wcmr1W9IETifM\nGpdOz5f16L2TFmTq0D088JCR2vVvNDAsFli94iIfrQ4kLDqARRvURJSJArKnmC2ZmsUr4yV8fd2f\nGiJJ0LdHHE8/KadaZe8Zq1fjZazeUJMvPon3KvHnhTq1JP74KZ36TaIQJRlJyRbAfc991+8KDh2L\nZNOX/41tL6/CsfuedP64Eznpug2aU7dB85z/fn/Z3Bv+vyAIWkAuSVKGIAg64DHAIxWa/8bT6gXc\nDm1td1XNXHOni+I9F2T1P/VUHHUay9H6BjOyyxFEyUDviSrKV7s1NCtJ8O6U4zR93EjlWt4RGZk3\n+m9iKgXQpE1EvsdElFUw7b1Y9u7OZM0bTjZ+cJoJ84KpVd8z5pMkGN//BE3b+lMmtnjTOoyBAiNn\nl+fyOQfvzfKja4s0nuqRxAsvxebknd+aewytrx+dvKQstv+vdM6drMjSn68z2+WLMGvyYQ7uqUZw\nuIbh03U82OLGlrG3Zh4kKEjPM90986hWv5+AKSuUmZOTvLJ+F7r0zqL94xepWf32bCV//GXD4dAy\ncsw1egyuRIfH9rJsrl+hBoIowrAJ/kyebELvLSvrNqM41d33AkpK8auYCAU2/btnK4B1kiR968kF\n7nqSzj0J606StKsv28fHx23v+eZrF4R3303j5Gk9MZUvMeMlI03bG2j9TFi+xU1bVx1FwJ+ew6M8\nWkd+2PXVFS6djeH1j93La9dtrKf2g3q++jiRyS/LeaT9EYZOqua2V712xSls1iCeH5q/QeApImMU\nTHknliP/mFk538yXH11h0Fg59RsF8/XnZZn/gfsznQuCKMK88dfoP1SN3tePb7emsuyNJFKuVaRe\n41AWrNMRWfZWjynukoNfvi3H59vMHq0jLU1g6cJI5k5J5MBhFecvWDh1JoMLl63EJ4gkp/qQkanB\nbNYik4s0qJPES33DqVfbXiD5rfvUTGJiOebNTOF2jJ53OmHoaB2jxqTS/QUNrR+z0KdnDLUfzmD7\negfRkfmvYdlKGQofgcGDbyXo0hruLsnq7rsRpTEnLUnSWaBOca5x15O0C7drSlVeqmbe6svOb0jI\n1asSI0dpAQsp1/wYvUSLMTD//t0r58z8tSOaqe9ovTI7NysDVi9UMOBVz6rDZXJo/3ww9Zo5eH10\nIPs6HWHB6ioYAwq2iK8liHy2OoyxCzReWf/NqFZfw/wNZfj1m1RWzLdiNWcSGpmGUhWNJBUsdekO\nVi0+jlrty8XzCbRuIOCjVNDhuSg6PKNDrcn/d5s+5AhPddVRrrx7G3VcHMx97TQ/7qiFJKmZPNuB\nSpWJTu/EYDASGCQQWV5G3VAfwsNVhEdoSEu1seULBT0GGTGb9YSHHeSJtvDCc/5EhF0fgmEyyZg8\nK4ZF85NRuz/uuliYOiMZvW8Ez/fKDvNHRUt8tUPNzKk2GreLYtLIwwzsfau4TEamjIXLy/HZ5w6y\njYnSt5nnhZv3kvuedMG4Eznp24H7JO3le+RGSama5YYkQaPGiUhSAN2GKKjZKKbA450OWDnjKu2e\n0xFd3gtDnYFZw/ZQrZ4/9ZoWTc0rPFrB3HVRvDvLSe/2aYyd6aRxq/w98nH9j9CwRSAVqpecFrgg\nQNPHjQhCPKvfUKFQORnVMwOnU4Ex4ATV6wk83qUGlWsoCjUUnA5IToKrl5zs+e0SW9bHIpM5OXzI\nwti5AdRqoCqU+LesP485K4zxkwo+0G6Dj9cns/JdCykplYgqE4LCx8nO3dfw85MA7b9/ecEByGjT\nLjukHxdnYfuXEXy9zcTbH0Tj45NC5Qon6dsjkLWfpFOtipx2bW7PxpiQKLD+k+qs//TGKIJcDv97\nzY/H2poY/lIlPtt+kk0f6NBpr9efjP6fQL368dSpYyAry54zaco1t/nmKurShNx7it1uL9HulP86\nSnmfdJFx15P0nQh3e1MTPK/r58aiRclkmZRMfEeNRle4S7Pu9X34BwbQuY97IysLw7YNZ0hOiGTi\n0uLNiFb4wOApZfl9RxrzXhVp2OwQ42bXuCVc/9nq86SnhfPCKyU7ghKyVcw+XOykx0iRhq0qAZCc\nAAf/rMjB3xKYOSoJU1Yget9TxFbOpGGLMlw6d43zpzK4liAnM90PqzUYu80fH1U6Gm0apgw1YVHp\nvLY8gIDgWLfWkZUB65f7sWSFBaUq71f2yGGJWdNOceRQTQKDVXTrHcAj7eQ8/7iO6TPT8PPz/BkM\nDxfpO0BD3wEanM4sDh1UsWljJJNmaUhJqc2jj/yBxWr0uE+5KOjRJ5mWrQSqVs/bsHyosZwduyRe\nGhBEzeYa1i6Lp8mDck6cUvDtj+U5eAh0uuyuCtfMZqvVmlNM6opQyeXyUhP6zgD89OoAACAASURB\nVCtqVlrWVhpxt3rSQiHEVfqbCQuBKIrY7XacTicZGRkYjZ71lXoCs9mM0+nE6XQik8nQ6XRetdDT\n0tLQ6XQ5UqFnzojUqeug72QF0RUL34QP/ZHIp2+qeH2DEaMXRkYmXnUwvmcGo+aoqVzH/UrjwpAU\nL/L66Es47BksWluBoJDs7zA1WaR3u0yGz9ZQrV7Jj6FcNGEPqdeMjF9aPt9jTJlwbK+Jfb9e5dJp\nO77+EByuIrysL5HljASFyzEGZhshe3YlsHaBnJXbjRQQ1b4FY3vvISTQl7dX3fjsZmYIvLXkEps3\n+WKzBtH0kRR6DgwnOib7tx354kEQDaz7xHt5TIcDmj9o4qluPvz2i5kL5wyMHn6OAX38SkxZ7rsf\nbLw8Ipqdu+3ofQvfkj5cbeKNuYF0br+P/YcjaN1GyaxZeRf8uQxqlwEsiiIymewGb/tOEWNmZiY6\nnS5nbe3atWPXrl3/RaIu8QULgiB9t7/kBJPcxaO11Uhedunvek/ahZL2pCVJwm6343A4crznknyZ\nRBHatU+iwSMC0RUL94otJvj0TYE+Y2ReIWhRhJlDjtHkMQOV63g37BwUKmPW6jKsWXiRvp2yeGlc\nBm2eimDCwEPUejCAavW8U2FdEM4cM3Hkn1imrSqY4LR6qNdMS71m+RM5ZE8R+3CRlb6jtR4R9O4d\niVw6W54161z5VLDbYfZrF/hiYyXKlNczcnIQTR/RIJdfN5T+2JXKsUMV+O4nG960tSeOPY9/QDDD\nx2gYMVbDTz/YmDYxihXvpbJ8schDDb27pTgcMGKML6PHpaP3dS/53eMFLc1amnm+S2UcDiVTp+Zv\nwAqCgCAI+Pj4oFAocoja6XRit9uxWCzIZLIbiPt2hMbz26v+gwR92yDepZ70XU/SN4e7S6KS0+Fw\nkJWVhSRJKJVKVCovNB3ngdyGxvgJCWSaBdr2dC9s/c7/9lOtrj+NHy1eWNqF1QsOIghGug+P9sr1\nboZMDr1fiaZuk0xWvObL5x8eJymhDBOWekcvuyCIIiyecJHHuhnwD/JO3v6DeXsJCTPwSEf3Izk2\nKyybYWfiFCu+vtnP1KZPU5gzU4d/YBBL18qpVO3W4Sk2G7w21s7YiRYCAr1X1XXiuIPvvq7Kxu22\nHK+5RSsl3/0K76/Q0rOvP+XLHWH1u4GEhXpHk2DytGsYjJE8292zzxEWBpLkw7JlDo/STa6Qt2tm\ne27SdjgcOeNib/a0S4o875Oy+3CKd+d3VTqrJUoAJfGwu0JlGRkZqFQq1LehzFWSJPbutbNihZFe\n40PcEpDYsfEUGakRvDytYG1rd3HmqIlfvi7DqPnhXtGvLgi1G+mZ+o4/l89XBMlCSmLJzxT8ZMVR\nFD5a2j3vnbz35fNWDvwey4TXoz0KCb8xYS9ly5p5qquKw4fsPNI0jrmzAxgxScOaL8OpVC1vG3vq\nqINERVno9pz3nkdRhP4vpNO9dxJlbmq7l8thwMu+fLfbSWTZIBq3CmfoyCQs1uK9c1fjZXzyeU0W\nvanxOJQ+d2YGMTFpdO5ceFqkIMPdRchKpRKNRoNOp0Oj0SCXy3E6nZjNZkwmE2azGZvN5jVlw5vX\nZLPZvKZKeLdCku78X0ngrvekcyO/FqaiwOl0kpWVBYCfnx9yuRybzVaiIXVBELDZoNMTmbR8CoLC\nC9+AkuLs/LQplPGL1KjU2ZXGaSmQeg0un73GuRNxXL2Yid6g5LGutShXWVEg8dttMP+VeDq9oCU8\n2jteZmF4a8peKtU1EhKpZHI/E516XaRjD/eKrjxFSpLIji8iGP2GBpkXDBBJgmWvnqRtVyOhke7H\nuU8czh4a8vEmK92fPsXRw9Xp0kPixSF+FLRXH9yTxT+/VeLrHywIgveexfmzLyNXBDNkVP7PnK+v\nxPylAZw9bWPs8DBqN9QzZuRF+r7gW6R89XMvpNK6DVSp5tlzdvGCwObPI/jrL+8rDLq8ZplMlkOa\nLk/bFSKXJOmWCvLi7jn3268Kx91aOHbXk3Tul8MbeWlJkrBarZjNZjQaDSqV6oZ7lDRJD34pEaVO\nTosnCxchOXnQxJrZFmRyM2+MS8ZhD8Bh16NQZqJSp6PRmfHzV2AICiHlmoP5ryRit+owBh2nTiMt\njzxVlfBo2Q0b7MIJ/xAUFkC757wTNi8MO764QFJ8FH2mBqJSQ5X6FtbO07Nn1x7GL6qHynv1agDM\nH72Pek0DiankHQPkqw2nEZ0B9Bzq/vfldMKskXHEVnTS7alw6j8Uwsff+WAMKDjU73TApGGpvDxc\nIDTMe4V1cXHw0boKrPnE6lbkpFwsfLrVnx+/szF1YjTrP77E5k/98NW7T5obN5mIiy/Phk0inubU\nRw3NpHt3MzEx7gnrFNdwd+Wsc5P2zRXkLrJ2txjt5jVlZGTcJ+lCUJpbsARBkAN/A5ckSeroybl3\nPUnnRnFJ2uU9S5KU4z3ffP2SxM6dNrZsDmLUYm2+nondBj9tPsvvX4mYTWGotXKeGhBEcLgaX3/Q\nG0Au9wPyLohKuwb7d5fj4G/X+Hl7KuAkKOw0jR4NR++r5eTB8sz9d3hGSSM9VeSTFVq6j1blaGnH\nVFEzdpmatfOyGNH1IqPmGKlY0zt6xj9/dYXUpGjGL/FO3tuUAd985M+kRSq3RVckCaYPPUlGegyZ\nhiu8tU5BhSqRbp07c8JhAgKM9B3gPYKWJHjhuTjaP+FLleqedUY8/KiSh5rC6JeNPNBEx3tvJdGs\nSeEhW4tF4NWp4UydYUKr9ay+45vtNuKuGJgz5zYprOQBF2m7ujBco3Jd43LdqSDPS7f7PkkXDGcp\nnQv+L4YDRwCPN6t7gqRzh7mLQtK5vWe1Wo1arc6TkEuygjw9HXq/qKRDHzu+/rfeOzlB5It39nD2\naGX8AqByAzUHfxUZtcCAMch9RjUEQvOOATTvGIAkQcJlib27HPzydSbxl6IxBJzAYvbFz7/kH525\nI/ZRua4/lW6qHldpoN+UsvyyNYl5o0Watz9Mj2HVi2U4mE2wfomcXq+oUHppf1/66l/UfCCQmg+4\nN9by7HEr00ecIy25MgNHpdPthXC3P9ORAyZ+/aEiW781ezXM/f478WRlhTFhatHyoRoNvLXSn0/X\nZ9F7QAydnzjAvJmBBX6uQcMSiSkno30nz1rHbFaYPkXDooXibVNBcweCIKBQKG4g7cIqyG/G/QlY\nhaM0yoICCIIQBbQDZgKjPD3/niBpF4pCoqIokpWVhSiK+Pr65rxo3rq+u3jqqStExgrUb3m9mlqS\n4ODvyXz94QUyUitRtoo/z42Vo/MLY+X/sug6WPKIoG+GIEBolECbZ0M58OtVqtS7gM5Xw6QXTdR4\n4CQDJ9X3erjZha8/PktaciSDZuYfsmzaIYiKtR2smmHk0J/7eHVZLfyMRauFXDT+b8pWCqBeU++E\n8ff+mkTchVhmLC88bJ6VCXNe2cuxgxVRKPx4otslnuntvnqbww4TXkph8FCIjPKgv6sQXEuCt5ZE\ns/RdG8XV43n6eR0NG9vo36MsjR9O4svPNAQF3vquHDossuvX2mzfYcbTMPe82RmUiVbQpYtnkZDb\nrd3tTgW56zi73c7ly5fJyMgo8gSsixcv0qtXLxISEhAEgQEDBjBs2DCvfZ7SglLsSS8ExpBf+LIQ\n3FMk7QkkScJms2EymVCpVOj1erde5JIg6eXLU9l/UM8rSwP+vQf8su08P3yqQCaXU7tFCHUfFlCq\nIpAk+HDWSSrVMVK/hXfCttvWHMOUFcrLI0LxUULLLiKfLjUw/KkkHuuWzJO9K3l1TGHqNZFNKw30\nGq8sdOZ0aLSCV94M49OldsY8m8iAVwXqN/NMnnTv7mucOxHLzLXeEbqx22DtGxb6vaJBV8C+6nTC\nh8tOsO2TUCpU96fJ4wkc+l3NkPGerX/GuMMEBRnpP8h7BA3wwvOXaP6wgYaNvNMHXzYGtv2gYdIY\nPQ+1NLJo3kU6tL1u5UkS9Oov0evFBMLDPfMaL10U2LQxnD///O/pL+VF2q5K8aysLNq2bYvVaiUy\nMpLg4GCaNWtGzZo18/S484KPjw8LFy6kTp06ZGZmUr9+fR599FGqVq1akh/rtuM2jGbwGIIgdAAS\nJEnaKwhCy6Jc454gaU/D3Z54zzffx9s4f15i/HgtL0yUoVRDwmU7q2Ycx2YN5tEeSsrXVN8QOvzl\nizPYzKF0H+ml9qEzZn7ZHsmgGaocwgwIkTHwtXKcOWxh4zI1P24+zYtjjdRrUnyREUmCuSMOUL2h\nkdga7vVgK3zguVHR7PslnXdmQmjkXwyfXZ/AkMItB7sN3p1p4ulBevR+3vn93pu5h/BoI6075d/D\n/ufPySydno5KrWPEHB3GICNT+6WzZI0MuQdv5cF9Jn77qSLbvvNumHvNqkSSkqJZ/4V3e+x8lDB3\nsT9fb7UwYmw5Nm89zIolgcjl8PriNCCSoSM9D62PHpbBc8+ZKVfOvWIxF1z7QWnqR3ZVkMvlcoxG\nI4cPH+b9999n//79HDhwgGXLllGjRg02btzo1vXCwsIIC8veD/R6PVWrVuXKlSt3HUnfiT7pI3t2\ncmTvzoIOaQx0EgShHaAG/ARBWCNJUi9373HXy4JCtjC9i3jlcnmB/cw2m42srCxUKhUajcajl1eS\nJFJSUggICPDGsnE6oVr1RKKqwmPPh/PJ0n0c+6cCNZsl0/SJ4FsqbePPm/l0sZKhc9RElit+T6XD\nDtP7nqPx4xpaPZ23dydJ8Pu3KXy7QcAQcJ4Rs2sRFlV022/L2tN8t1HL2LdCCvWi84I5C758/wKH\n/gykWr2TDJpcv0CFr8UT95CcYGT8m+W9Ugx35kgmi8Y7Wf65jsCQWy+YeFVk+tADJCbE8OSLAi06\nZj8rU148QIPGvoyZ5r5x5bBDl5ZX6DtAop8Xvejka9C6uQ8Ll9to3KzkenMTrgr065GO2WRi7Xs+\ndHo6mPfWmKn/gGdhma+22pg5TcuJE2qPc9GSJJXKoixXO6dLGOndd98lJCSEHj165Pz/oswEOHfu\nHC1atODw4cO38zPfFlnQdbvufLy7ezNZvrKggiC0AF65X91dAArypEVRxGQy4XA40Ov1xRIO8FaO\na9SoBMw2CCsjY2a/qxiD/eg1SYZf4K1hbIcdvlieyaNPa4gs551q55Uz92IM8ufhrvmHXwUBGrXx\np35L+GptFv/ra6JKnZMMfa2+xySbGOdg64eB9JnkUySCBtDooNuwMrROEPlsmYHhnVNo1vYKzw2p\nfkuF9cmDmRz+J5ZpK72jOy06YcW0OLr18SUw5MYNMCleZMXsfez/qzINWgbxyuLAnIr1betOYrMG\nMWKSZ2Hl18YeJjjEQN+B3t1se3e/QJMWRho3846xmR9CwiQ2fePL7KlO2j0VTWyFi9R/wLPPYjbD\n9Ck63lpWtGKx/8os6aysLHS664ZYUQg6MzOTrl27snjx4lJnlHgD/xHFMY8d33uCpAubhOXynpVK\nJQaDocgvrTdf9l9+sbJylT86wxm+XB1Gq2ckKj+Qf/h08/KjBEcE0apL0cZF3oy/fojj3IkYXlli\ncIvAlCp4ol8kLZ+S+HC+P6OePs24xVFExbjXQiOKMGf4ceq38CXGzZajghAQIqP/tHJcPGVj4zIN\nuztd5qm+Th7tXAZByI5SLJkUT/vuvvgXo7guNzYsPYhW70fn3tlGlCTBHz+lsnrxWZISqlCpppHJ\nb+sJibheP5J6TeSbj4N4/V2hQJGSm3Hwn0x+/7kC276/PrrRboO0dBlpqTJSU+DC+XQuX0qnUdMQ\n6taTuVU3sG5NEvHxMXz4+e0RI5TLoWFjgS2brFy65E+PZ07x3uqybhPua1PSqVxJwRNPeOe5Ly24\neXxmVlZWkQvHIDua2KVLF3r06MGTTz7pjSWWOpTGnHRuSJL0E/CTp+fdEyTtgiAIOaPpIPtFMJlM\n2O32YnvPue9RXOs8JUWibTsJh0MgoryOlk9rC/Qs9+y8QuKlckx8O8ArHmF6isjn76h4ZpgCvcGz\nCxoCBV6aXZYdn8QzfaCFDj0u0qlnhULP+3DxQSTJSIc+EUVddp6IrqBk5MKyHPo9ky3vZ7H1w2P0\nGx/Gnz9eQKs38Fg372zu8Zfs/LGjDG+s1WA2wdo3D/PzN/7I5Qqad4yidWc9Gl3FW85bPG4fzVsb\nqVXPPQ12hx2+3JjAsrlGlKoUOncQcdh9sdv1iKIPPkoTSmUWKpUJrc6OVqdm3VoBi1lLWPgR2nXU\n8Ozz4QSH3BoaTEsVeGNuOG8ss6HR3B6Stlph6ngNoyZbadrKl7EDg2nRyMq7q6BWnYINvOPHJL75\nKoL9+27LUu8oMjMzi0zSkiTRt29fqlWrxogRI7y8stKDUlzdXSzccyTt8qTtdjtZWVn4+PgUy3su\n6B5FgdPp5IknL6HwCeCZ0QKB4QW3BKUlOtm9JZh+k5RovRDBkiRYNvEI1Rv4Ua1B0YZnCAK0fiaU\nSnWtrJnjy75f9zBuUb2c8O7NOH/SzC9fl2HIXE2JaYHXeEhPtYZ6ft0m580pEg5bVWo3PsG5Ew7K\nVlAUSwJUkmDJxGM0aB7AoilHuXCmBpExGvpOCKJa/fx1p7/beJas9AjGTCu8TevEUQdvzjnI8cNV\nkUQ1/gFWxk4PIiBIjq9Bws8gotVZyRY2ulWsJj5O4LutZfj+qwxWvqNHpY6ncpVL9HqxDM2aq1Cq\n4IXnL9CoqYGmLUo2zJ0bo14+TVRMEI8/mX3PZesj+GhlMr2e19Pl6RNMmhqV5/cnSTByiI0hLycT\nEVH09f5Xwt3F6ZP+9ddf+fDDD6lVqxZ169YFYPbs2Tz++ONeWWtpQWn3pIuKe6JwzNV/aLPZsFgs\nOTrbrpGS3sTNM5/dhUswZdmyZGbO1vPCFA3KQiLFTies+t9l6jXX0clLHuinyw9xbI8/o5dEuK2S\nVRCsZlgz9wJXz8sZPT+Q8lVvLHByOGBkl9M0elxLqwJy396CKMKcQacIjtQjkEncBT/sFj/0ficp\nV9VO8/Y1ia2hLjByIYqQkZotIHPhVAK/bE/gyrkKKHwsNGyVSfse0YWOA01LEfnfC6nMWiZQ/6G8\nrZfMdFj11km+36rBZgvkgWapVKtjZPVigQ3fKAkqYoedwwGH9jrZvimev3f7kJYajFZ7CbMlhJ1/\nONB6t5MrX+zbY2FATz/Wf+1D0E1FdudPOxndLxWlMokNn4USdFPR9ppVZtasUnH0iF+xDDuXdKdW\nW/LzyT2B2WzOGZ8J0KdPHxYsWEB0dMlMnSth3JbCsXe+u/N0NeBR4f486eJAFEUcDgcymQyDwVBi\nc2GLKphy6pTItGlBPPmSo1CCBtj67lF0hmA69PYOQZ86mMY/O8sydL7aKwQNLnWwMuzamsicEQ4e\nefIo3QZVzfGOlk/dg6/Rn4e9lEsvDFveP4LCx4/uY4KRybJZLisdTh8sy9G/Elk5NwFTZgha/Wmi\nymcQHKnj6oUM0q7JMGXqsVmDsdsCkCssqDQpqDVWkhMq8fizDtp1D0AuL9yrkyRYNGY/TVoZqP/Q\njWFupxN2fpPKqmUXiI+rQZnyavqPC6NBcx12u5EB7a8wbKKCoOCiG5cKBdRpIKdOg+zn5vxZkRef\njECtsdDhkUTmL9VTv0EJqdT8C6cThg8003OgQFDIra17ZWPlbPg2kDmv2nishQ9TXovnic7Z321a\nqsDShYF88YWz2JGXe8GTvlcg3g93/3fhyj1brVZkMlmJPuyevvCuojWZTEXnLlZqtbAQXr7wjf7I\nHwlcPlWeCcuNXhESsZhh1WwT7Xr5EOyhkERhEARo3jGYSrUcrJxp4OCfe3n1zbqcOpTMob/LMXpx\n0aYkeYqrl2zs2VmG/tOVN3xnOj+o1URHrSbZLqTVDGePluHoX/FcPO3AGBJG2WpaQqIMGIPl+AVI\n+ChVQBhvjTtMg5bxdOzlnvQnwDcfn8aUEc74GdfD3E4nvLvoNF98FIJG66BVp2jaP6vB13A9nz/r\n5T3EVjLSsat7+Wt3MXn4CR5qbuR/CyLZ8J6Nl17UERN7jDffjSW4hGynWVPOo9UF0b1//r31Pj4w\neV44u77PYvqEMLZ8cZIV75Vl7Kg0mjfPpFGj2zPkpTSgNLaJlTbcJ+n/MFzqPTqdDrPZXKL38kQw\nJXfLV5++SYgyaNyhcDGGjFSJHz8x0GO0D75G77DbWxP3UaaikYce844ISl4IK6tgzJuhbFhgYWTX\nOEBO+xdk+AWUPEOLIqx67RwNH9MTHFnw5q7SQJV6KqrUK1Pgcb9uO4/FFEb3Ee6TZmqSyPb1Acx/\nW5YTLdmxPYlFMxxodb5MWOBLtbq3PgM/f32VcyfKsXGHd0WpN6y6RFJiFMs2GJDLocfAQJ58Dt6Y\nGky7lkratD/OlJnlitwSlxcuXRDZ8nlF3v5Y7paB2ay1jo/qSbzSP5gmDZxIUhgHDzpwOBxuTZT6\nL+JmT9o1/vI+8odTvPPh7pLA7SnhvMNwyXrK5fISHSUJ7pG03W4nPT0dQRAwGAxs3WplyxYjHQcH\nFepRiiJ8uuAC9ZqZqN7gumXtdGRPsLp0GvbsSufvncmYs9xb81frT5CaHE73V9z3BosKHyX0Gl8W\nnSEdu93AxVOXb0vBx5b3DyNXaGn1tHe8r4xUkZ+/CKTfq0a3CUySYOGYAzzcJoXaDyg5fdzGs22O\nseA1NT2GGFj6eTTV6t6a58jKgHfnKpgwS8TXiyO8kxIl3l8SzNQFatS5ott6P5iyIJK3P1Vw+FAA\nzRvY+Hhdkld+J0mC/j3jaPtUKuUruU86xgCB5RsiQNAyYUISRuP14k9XlMzhcHj8fpfWcPfN+K+s\n805Cku78X0ngnvCkXTJ7JTkAIzfyu4ckSZjNZqxWa07R2tWrEn36yHmshx2db8E/h80KH79xHlNm\nEGeOnmF6n2vY7UYcdn+cDh0Kn0x8VOmo1GZEUc6nb+lQa84TVSGVZh2qU6GGDsVNXWZXzpr5aXMY\nA6YpvTb9qTD89vVFTBn+PDvGyrZ3/Hl96BEGzaiCbxGHYxSGhMt29uwse0uYuzj4cN5haj8UROXa\n7lcWb117HJslmP4jAhjS8wAnjlShTZdgnhsUWCDRT3tpL3UbGGj5mPfC3JIEQ3qeovmjftR9MO+a\nhrKxct7bFMVP32axaLqM95bHsfCtAGrU8mx8ZG6sXBGHyRzC0Ame64Evnx9PdLTE8OEhOcZsfhOl\ncs9vLqnak5JEblK+HXvW3QCn806voGRwz5C065+3w5POCw6H49/c8/WiNVGEx9rEU76WSPla+Zfq\nJlxy8OPHR4i/UBuJilR/MI7gqBgCQvT4BfigM0ho9HZkMhVw/Tp2G5w/FsGR3+V8tCQZc5YcveE4\nFWtB8441CY6QsWJKPC2eUBMV6x2VssKQdk3kqw/96DhAJDRKxgtTAvh+nZ3Xh6bSeZCd2k28m2cU\nRXh/+lkaPFp4mNtd/PHNBbLSoug52v3rJSeIfPdpKA80vszzbXXUrB/EW5v0GAIK/t63fXSepPho\nVmzwbsn1qrfOYcoMYfT0wo2MFo/paPKwjtVvOejzvC81ah1l+apYVB5y9bUkibffjGLe23KPhFsg\nu9p7+6Ygdu+24XDYgey5ze5MlMp9zM2kXRo91Pz2qNK2ztKG0hjtFgRBTbaAiQpQApslSZrgyTXu\nCZJ2IbdlWlIP/M2GgCRJWCwWLBYLWq0WpVKZc+9x4xJIvCan+6Bbi2ecTtj/81X++d6MzRJFZIVA\nZHIL7XqbqNogdzVP/k+mjxIq1PKhQq0oAEyZcGpfFMf+usZbr6ZgtepRqVQ06XB7CnBEEd6efIwq\nD+goWyX7M8jl0KZXKOX3mvh8hZoDv+7j+dF1vNYvveX9w8jlRh7p5p3PmJUu8sNGfwa50SLngijC\n7CHnEMVALp7XMPN9LTEVCp9al5wosmG5gdnLJLzZIRR32cm69yJZsFLu9ghKhQ/0HR5M114SE18K\npnXjDN77UEXlqu4nq/v1uEDjhwOo08CziIAkweQR1xg4UKBSpQBEUcz5g+w2KlfO1lPSliSp1Hqq\n9z1pzyA6S9/3JEmSRRCEhyVJMgmCoAB+EQShqSRJv7h7jf9eHKiYKGlvOvf1nU4nGRkZ2O12/Pz8\nUKlUOS/ezp0W3n7HQKeXbuzzTE+R+PKdQywfY2Hvj1CjiS9dRpq5Fmehcr10qjYoeoWnVg+1murp\nNrIsTZ9IReFjxj/UzOwBKXz78akSr47c/N4hRNFAq2duLRmuWFfLC/9TknA5gLmDT5J01VHs+129\naGXPzrI8OyrIa2HudfMOU/2BdKrVd481zxw1MarLRUxZUQyZIrBgQwwxFQq3jSUJ/jfwCA8/nkqD\nxt7LQ0gSDOt1jjadUqlW23OFPYO/wJvrI+ncXUmPrjreWnTZrfM+WptAYkI042d4HrL/ZHUKNrOC\nMWOUZGVlYbPZgGz9aqVSiUKhQC6X3xD2dhWLushbqVSi0WjQ6XSo1WrkcnnOsQ6HA4vFkjOI506T\n4s1OhNVqLXAo0H1kQ5Tu/F9ekCTJ9O+/KgE5kOzJ57onPOncD/ztCHmLoojVasVkMqFWq1Gr1Tes\nISUFunR10ryLDWNQNukmXrKzfeUp0lOqEB7jy2Mv2AkIzSaC37ZcQCaLoG1v78yHTk10svOzIDoN\ndFK2ShgXT9j4dq2aP789S5fBBqo+4H3FqfMnMtn7cwzdxwn5qnvpDdBjQjA/f5HIkldMtHk+hSbt\nilbMJoqw8rWLPPi4jpAo7/QR/b3jMmnJZRi/tPDfIT1FZPnUf7h0pjKiGMTMdyRiq7lvYK1Zcgyn\nI4Cx070zy9mFN+edxuEMYOhEz0Y65oYgQK+XgniwuY3xg0LZueMcH3wUk68ISka6wMK5IUxbKL+h\nQM0dpFyT+GCZnu3bJfz9FTlaB678M4BCoUChUKBUKm8wkAvztH18fLBY1DNmVQAAIABJREFULAiC\ngEwmw+l05hgAucPjrnqWO4WMjIxi6XbfK3CWQk8aQBAEGbAHiAWWS5J0xJPz7wmSzo3bQdIOhwOn\n05nnLGpJgjaPXyWygpPqD4Vgt8H2lYe5cLwKlesbeKxZJj4qf1xh7IsnMjh/rAr9pim9EgIWnfDh\n3EvUbKKmbJXsjTq6kpI+0wLZvyudj5cKGPz30nN8TYLCvPN42G2wenYqjdrL8A8tmHQEGbToHEy5\nGla2vevL4d/38eKkOh63AG1cdgCl2t9rA0cy00W++8iXAZM0+cqbQnaV/YY3D/DHjrLE1vRHo42n\nZXstsdXc9yAvnLLy7WeRvPOxZ0M3CsPZUza++Kgsb66X31JAWBRUrqFk/bdKJg8x0bqJhWXvi9TN\nI8LQv+dp6jYM5KHmng9OmTo6jrZtBR58MLs10EWcKpUqJ5TtcDhyvGG4Ttq5tfhdRO3ytnO3NAmC\ngI+PDz4+Pjnhb6fTeQNpu4rQXDntkiTtvIRMck/Auo+8UVqzApIkiUAdQRAMwDeCILSUJGmnu+ff\nMySdm5xLiqRdsqOCIODn55fnizz5fwmcu+hDz1cD2fdzHL9u9sU/xECnwSZ0fnpy55jNWRK7Nxto\n08OKIajoFbW5sWn5YdTaAFp0vtGTEmRQp4Uf1RvBT58FsGS0lQo1D/LMiLoFkpI7+GDWXvyDjdRr\n5X4PdplKKvpMg80rDMzqH0+rrlaadijjlujJ+ROZHPqjPINnqRC8Vc095wg1GgZQo2H+Hujub6/w\n6QonvkY9/acq+e2rTLR6f7q/7D5BOx0wfehFnn1RTWzl/IU+PIXTCSNeTKBrDy0VKnsnIgOg0cLr\nKyP5bG0KA3pp6fLMKcZNvv47bd2UwoVzsbyx0nOS+fk7E2dP+vP9V3k/gIXln3OTtlwuv8Fgdnna\nzn9Lgu12ew75ymQyZDJZDsm7jnOFx10Ef7tI+76QiXu4E33SZ4/8xNkj7g22kiQpTRCEbcADwE53\n73HPkLQLJfEy5Z6mpVKpcDqded5n924rSxYbebyPg7UzTmK1hNG4k5Xoyn7cXAAmSfD92gRiaxqo\n0cg7rTeHfkvg/LHy9J6izJe8fJTQ+rkQGraBb1YbmNU/hSbtr9G6W4Ui5XX/2nGJy2fK8eJUpceq\nYiotdBsVxumDFn74SOTnLafoMjiQKvXy98YdDlgzJ5mWT6nwD/GOtOWv286TlR5B7zF5GxkXz1hZ\nMeUYZlMY7XurqdnIl4snszj8ZzkWrNN69L0tmrQPo78/fYd6j6ABZow/hlYfSJ/h3iPo3OjS05/6\njRy80i+U3bsusu6zMsjlEjOm+DF+Bug85BiLGV6fAm++6cRdJzI3abtC3zcXjUE2aQuCgM1mw8fH\n54ZjcxP3nSLtmz3p++Fu9yDdAcWxmCotiKnSIue/d37+2g3/XxCEIMAhSVKqIAga4FFgmif3uCdJ\n2puetMPhIDMzE4VCgZ+fX07o7Wakp8MTT9jxC45n67tRVKyro24rCXk+ccc/tl9EEsPp0Nc7m2pG\nqsg3H+po+6IDvaHw2LFfADw9MpyLJ218s1rL/l8872VOTxH5cpWedn1ENPqib1qxNdWUr65m706B\njxaDr2E/PcZWIzTq1u9u3ev7MAT406hd0XOuuZGeIvLzpkCGzLy1mjs5UWTV3L85d7wyDz4WQKun\nA1AossdJbliQyjP9NYRGub+57vsthb2/l2fdNoXXCt0A9v+dxa7vK7Bqi/f6xPNCTAUF678J4rVX\nrDza1EF4RBxVqvvSso3nYe65k+KoWg26di26At7NpA3X60VsNhuCIOQIoLhC5C7kriB3kXZuwr6Z\ntF3HWa1WRFEsFmnfTNL3PWn3UEpz0uHA6n/z0jJgrSRJOzy5wD1D0rnnPHuDpG9urVL92zSa18so\nSfDgQ0lkZvrho5XTcWAWemP+L13cWRPnDlfmxSk+yL3wC0kirJtzlsr1tVSo5VmONrqikhenKflu\nrY3Xh6bS9WUHNR8q/BqiCCtePUbl+jrK1yh+XliQQb1WBmo1hV+2+LNsvI3Icgd4fnTdHMPh+N4U\nzhwuz5D5Wq9ogUsSrJ19jHrN/alUK7uYThRhz64kNq86R+q1KsRWD2DkIg16w/Vc7EcLDxASHkDH\n7u4bWBYzLJxkYchYGSq1H5fOC2SkCyQlWLh0/hpXr6STlGAhLVVEo5HTrXdl6jZQFToIxWqFCUNM\n9B3uJCzSOymTgqBUwWtLI1kyI4Etn9SmaasDOJ14VE+x7y8bf+wK4sgR78pgSpKEzWbDbrfnTKrL\nndO22Ww5XnF+pO3yoOFW0nYdnzunfTNpu3LbnpD2fZJ2D3e6Kj8vSJJ0EKhXnGvcMyTtgjdI2ul0\nkpmZmSPrmVscIa/rz5yZxIXzfjzYPpnYWr4U1Ntstwrs+kzDI89YCAjxzqa6beUREIJo/VzRQqhy\nOTzeO5Tj/2SxcZmag7v38+yI2gV6ZZvePoQo+dPqWe9WiiuU0LJrMA3awA8b/Jn/sokaD52hfe9a\nfLTYQpvnlV7TM9/5+Sls1hC6D48gKwM+e+cAe38JROEDDVpH0KitCpXmxurzo39f4/zxWN783L2h\nIaZM2Pj+cb7+LBinI5SFM2S8OdeEjzL7T6W2otWL6H21+Bp8iYjxISPVwfQxWZgyfQgOPUqrtno6\nPx9DUMitz9X4l44QER1Il57erRIvCGYTfLNFQa9haXy90Z9urc+ybF0ZwiIKJ127HaaPsTBjhkhI\niPc0UF0pKUmS0Ov1Oe+sTCbLaeWC65PynE4nJpMJURRzCDs3uRZG2rlJ/uZCNFEUbyhEu5m074e7\ni4ZS6kkXG/dJ2gO4Zj6bzWY0Gs0Nfc/5Xf+vv2zMnefH4y+mYwwpuKRWkuC7tZeIrhRAnebeGT95\n+mAqx/fG0utVeb6tT+6icn0dEeXhsyUBzHvpGINnVsIQeCtTnz6czv5fY+g+QfCaKMnN0PlCxwHh\nXIsT+XatntkDLPionKh1cmwWii1xmprg5LevIujcT2D2kD9IvFKDiHJqnh1pJKZq3vl1qxk2rZDo\nN0bEWMDQENEJu3dc49P3zpJ4tTp6gwqZzIe3vhAIDJWQyTSABijYwElOgp+/juGXb1L4eLWIUpVI\npSpX6Na7Eg820fLLj8kc2hfLuq81t2XKmAvjBx2kXOVAOjwXRrtuBt57/TI9O9gZNCqOLj2iCjx3\nycx4IsJg4EDvjd9yjYKVy+VotdoCvVgXaec+N/c8ehdpu7zt3KTtImNXustF2IBHpH3z/pSVlUVU\nVMHf232U3uru4kIohLDumo/tso7NZjOSJHk85N31oouimDOsIy84nU7S09Px9/cnIwNiK6RTqWE6\nld2Yz7vvxyucORjBoNn+Xpk6ZDXDW2NTadFVoEYj74XLRBF++CiRo3/58UTfLOo/fD3naLXAnIFx\nNOooUKe5F6dBFIDDv8fz4yeBlK2SQMJFOaaMSFSa8wRHXqNO81gq1/VH7UbxkcMOGamQlijyyZIE\nHA4tPj4idVtYadopDF0hzsw7k/cTEBDI5Dfz7u2+cNrB6kV7OX4wFo3ORKM2Sh5oEcK8YSmMm6ek\nXuOiy4o5HXD0gIMdWy6z/w856WlBSKKMnoNS6TX49nnRO79JYt4kLSs2G9Hn+vkP/mVm/ngT5WLP\nsXBljTw7Bk4cdTCsJ+zfLyM62jtWhcPhwGQyoVKpblD7Kypyk7bD4SiUtF292nDd0wZukSZ1kbar\n6lwQBCwWC7/99htHjhyhYcOGdOzYsUhr/vrrrxkxYgROp5N+/foxbty4YnwDRUKJm4iCIEhj3zYV\nfmAJY95ALZIkefXz3nMkbbFYcsZWugvXzGeVSoVGoynwRRdFkbS0NIxGf5q3uEJcsoMW3Qq/17U4\nG9+t8afHeBmhZYof4JAkWDXtKL4BBp4YVDKyn6cPmvn6Axnlqp6jx5g6yBWwbPw+5D4GOg8tuZGX\nuZGVIbFqioVHnnVQrkb2zu+wQ9xZidMHEok7I5CZGo1SdYWgiKtUaRCFOdNEwqVUMpJFTBkqbBZ/\nHPZAnE4dCmUaktOKhIHOg0WqPqBxq9hq91cX2PWFL8s3B6HJ9XNnZcCnK4+x6ysFVmsINR5Ips1z\nZYkqL0eSYFrfA1Sr7ceI6dFe/V6GP3cIU1Ywack6KlU9zoxltfArYZvJbIKuLVPoP1ZN87a33syU\nCbNHnefiGTlzV+ioUee6UeJ0Qve2yQzoJzF+vHdSJK6WSI1Gc0PPtDeRF2nnzmm7hFBy92m7kB9p\nu1rHzp07x+jRo/nnn3+IiIigffv2tGjRghYtWhAQ4N535HQ6qVy5Mt9//z2RkZE0aNCADRs2ULVq\nVS9+C4XitpD0mOV3nqTnD/Y+Sd8PdxeA3DOf8xImKej6s2cnceSomg6DCr+Xww4/bpBo0iGD0DLe\nab35edNpstLDePaVwjWii4rYmhp6T4HPlwYwd/Ap6jSTcy0+ij7Tbo/wgiTBxkUnianqS7ka16u5\nFT4QXUkgulJ2yNTpsBB/wZ/T+0X2/JiFUiWhM/oTHqvEP1SPIVCF3iih0WWSHC+yaZmeAdPlhEa7\nVxOQlizyw6f+THhDlUPQNiu8PecAv+8oR3hZH7q9HEHtxjrkcmPOeZ+/cxSHLZCXJ3vXoPly/QWS\n4iNYtikIm01ixYwgurWy0K7zBV4eV8krxYh5YdzAg5SvEkDztnkbhVo9TH+7LFs3JDKyj4K2Tx5n\n5OTKCAK8uygRrQbGji1+Vb6rqNPhcKDT6Up0DvPNld6SJN0gruJ0Om8gbVf++eY+bVfbpmv/UCgU\nVKlShW3btjF69GgefPBBEhMTeeedd4iPj2fQoEFure/PP/+kQoUKxMTEAPDss8+yefPm203StwXO\nktY1vkO4Z0ja00lYrlm1Pj4+GAwGj8Jke/eKzJ7jx2O90lH4FH7ejx9dICg8mAfb3krQkggWUzYh\nad2sHbl60cLf30fxzGgBhRfC5gVB55ct5fntumv8uj2a2s3PoHQntuwF7N56DqsplJbdCg4TyxUQ\nUV4gonx+BJD9cotO2PZeKk3a6wiNdi8nKkmwavpJmj7mR40HjEgSbF57js9W6QgO92PsUh0RZSve\nct6ls1Z2bfs/e+cd3lS9//HXyezeiw4KhTLK3sgeskRQUXAjSxyoF5ELMpygrCs/EbmiKAgoS1BE\nlrL3kD3KKlAopYvuptk5vz96U1voSNqkg+b1PH14gCbne5KTvM/3M96fYOb8qLSpq1hqiomV//Vk\n0lwnnF3B2VVg8hd1uXFZz1cfeLBzcxLjP5TSa4BtWtTM7N52j+tX6vHN714l/p4gwKAX/GndycCn\nb/tx/OBVps+tz8bVPhw5Ipa7Rcx8Yy0IAm5ubhVu51nQvQz+Ee2CUTyzaJv/NIe7zaJt/tMs2mq1\nmi5dutCwYUPef/99q9YTHx9PWNg/UZrQ0FCOHTtm03OuKjgKx2oIRc18toacHIHnn5fTolsyXqWY\naYginPgrk9S7DYlodp1V8+6izpGiVTth0HtiNHhjMHggkZhNGO7hFxxHyx71aNDKq8gpTAY9rJuf\nTvt+MgLCbO/BXRQmEWIvaqjd6CbRRz1IiYvmqbeibGI9WRxpSQZO7Q7liTcMNjvOrtXXcPXwp8cQ\ny4uWtv54CUHw4dXJwZw6lM6imalIBFdGTXGjafuid5RGA3w9JY4nh7tQN9J2tQKiCFPHXOKR3l40\na184Dx3RSM7/rQtn75YM5n9iYOlX0Xy2KJLwiPK/eOpc+OIjGa+9L+BmYeAmpI6MRb8Gs2iGkfEj\njLzxZjoNy+mEZjQaUalUKBSKIos6K4OSRNvs728Wa4lEgl6vL1Rklp2dzf79+4v0XrD0+DUFsSrO\nqrQBNU6kS9pJFzXz2RpEEQY+fhf3AD0N2xf/5avXCZzdF8/1s34YdA3w9LuJWuWEi4cL/mEK3Lyc\ncfWU4eSiRemSiFSWV6yVmiAn9oIP+3/NYftyL5xcYgipr6Jd36aE1JUiSOCXBRfw9POhff+KEWiA\nzUuiUTj70PkJJ/RaA3vXevH99GSeetuTwFDb9+aaTLDhq0SadVIQEGqboqi4qzncvtyAt+ZZloMG\nuHtTzen94Uyco+S9F06Tdq8Oj7/sQ48nSp669f1np/Hy8eL5sbatFfjxy8vodL6Mfb/ozgBBgJ6P\ne9G5D/y0UMNrz4i0bH+ej+Y3w7kcozAnvXqeeo196NLPuopsmRxCwpUEBObw2czyCbRer0etVuPk\n5GT1jXVFUpRom6u8zY5oFy5cYP369bRs2ZIffviBL774gkaNGpXpeCEhIcTFxeX/PS4u7qGtFDca\nHeHuak1J4e6SZj5bw9y5qVyMdubx150oqubuXoKRE9tjSU9qgauHEolER73m12g/wA0oWO4qAvpC\nj5VIwD/EhH9I3lZFr0sj4YYXsRcFNnyViUHvjsL5DjpNJK/OlFVYy83lEyncvlKfQa9rEAQRhZNI\nn+GuXDiUy7ovpLTufZPOj9e16TH/XHEFucKbDgNsI9B6Hez8Gfq+qMPLz7JQvcEAK+ek4e2nYd7k\nEB7pE8CQV31Lbf06fzSVy6fr8I2FfdSWcjtGy7b1ocz83rnUyIJCCaMmhvLEcJGFH3ozpFsOb07K\nZNAw653B/tqUzI1rESzeZP17kXjHyMaVbuzbayrVlKU4zG2ROp0OFxcXi+pGqhLm7yODwZC/fj+/\nvFTE3LlziY+PZ9asWRw+fJjRo0fTpEkTq56/bdu2XLt2jdjYWIKDg1m7di2rV6+2x6lUOlVxJy0I\nQhiwAggg74v9O1EUv7LmOarXFW0D7hdpc4gMwMPDo8xFJmfO6Jn5mTuPvlw4D200QPTRe1w9IUWv\nCyKwtgsdHrvOnWvp3IuvT9u+ZUvCyRUitRsJ1G7kBYikJqrYsTIMqVTHT7Nv8fjYUIIsLHwqK6os\nkR0/u/HI41m4uP2jDIIAzbq4EFwvm73rfIk9f5mh7zYqd+8y5E0Fu36uHs9OEG02PGP7sqsE1vaj\n/aOWFXAZDfD1v2+gVtUlrN5t/jXPDS/f0gsGtGr4ca6WsZOU+PjbTqGNBvhw3B0ee86N8EjLCwV9\nAwQ+XlyP00dULJgusO+vC8z6pqnFOfKcbPhyhhNvfSgrtT3tfkQR5k5MZORIE82bl20XXZxBSXWh\n4A2GucBNFEWio6M5ffo0O3fuJCgoiL///pt9+/aRm2t99bJMJuPrr7+mX79+GI1GRo8e/VAWjUGV\nzUnrgXdFUTwjCIIbcFIQhB2iKF6y9AlqTAuWyWTKH+qe1yLlhU6nK3bmszXk5kK9+hnUaZlDVMe8\nPLRWLXBoYwxJt5vi7JJIWCMNQXUMSCQiqkyBv3dE0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3RkpvniH5zKoy9VTHGLyQSb/ptO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1874888f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf1 = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "            cmap=mpl.cm.coolwarm, linewidth=0.5,\n",
    "            antialiased=True)\n",
    "surf2 = ax.plot_wireframe(X, Y, RZ, rstride=2, cstride=2,\n",
    "                          label='regression')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "ax.legend()\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_2\n",
    "# title: Higher dimension regression\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "uuid": "5e345542-f425-4630-9eae-0a446927ad73"
   },
   "outputs": [],
   "source": [
    "import scipy.interpolate as spi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "uuid": "20200433-3e90-4bb6-be5a-8e6a1360989e"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "uuid": "6e3caa90-2a2a-4429-8536-ab25091a5640"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "uuid": "afdb9c45-1b12-4358-ba3e-a1bc3c4d32db"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "uuid": "7217594a-3398-4dfd-9d16-f90ee0f24bd9"
   },
   "outputs": [],
   "source": [
    "iy = spi.splev(x, ipo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "uuid": "89d96d0e-dabd-490f-acad-15bba904b546"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f18747a5210>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pW2E54Rt6LvuAu3ZBbi5ceim0aQM33+wVt+6neJOUfd4pk9vaTiYjAzp2jHHN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\nYHiG+0iHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f18748885d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, iy, 'r.', label='interpolation')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_ipo_1\n",
    "# title: Example plot with linear interpolation\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "uuid": "b9cacc73-786b-4c6b-ad5f-e4d22729c17e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), iy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "uuid": "3daf1f42-54d8-4150-aab6-5188d1c23bdb"
   },
   "outputs": [],
   "source": [
    "xd = np.linspace(1.0, 3.0, 50)\n",
    "iyd = spi.splev(xd, ipo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "uuid": "7ba1134b-ac71-4c3a-a0fc-b644c59effc6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f188f6f6f90>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ws2bAycDqUGskB9m5E3r29EtXTJ0KTZqQckNLJYVFBjc0mDaF51/L5MYboUsXv3S7vmse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\npaAgIiKlFBRERKSUgoKIiJT6/xearDHC/Q2wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1874167210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xd, f(xd), 'b', label='f(x)')\n",
    "plt.plot(xd, iyd, 'r.', label='interpolation')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_ipo_2\n",
    "# title: Example plot (detail) with linear interpolation\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "uuid": "c3d9f85f-671f-4353-beab-fad9db9f8aa4"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=3)\n",
    "iyd = spi.splev(xd, ipo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "uuid": "0c3e96f1-8732-4ce6-a6ed-bbaae732d950"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f1874144490>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rr0GvXnXylCIicZFw8xScc3OAbZUcllBrjd5+u3flqQqCiKSjoHsKDuhnZsvN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\noaIgIiIl/j9EaZiirPqADAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1874155550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xd, f(xd), 'b', label='f(x)')\n",
    "plt.plot(xd, iyd, 'r.', label='interpolation')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_ipo_3\n",
    "# title: Example plot (detail) with cubic splines interpolation\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "uuid": "8c67b514-160e-40e3-8f69-da81d7579b2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(xd), iyd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "uuid": "ecc6c2fb-faa4-4149-b71e-05ac5cddeb79"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1349319851436252e-08"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(xd) - iyd) ** 2) / len(xd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convex Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "uuid": "a09a918e-760c-4e9c-95b8-fe3b568dacdb"
   },
   "outputs": [],
   "source": [
    "def fm((x, y)):\n",
    "    return (np.sin(x) + 0.05 * x ** 2\n",
    "          + np.sin(y) + 0.05 * y ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "uuid": "1f4a147b-d9d2-42d5-8553-dd95d75d8251"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 50)\n",
    "y = np.linspace(-10, 10, 50)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = fm((X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "uuid": "b3a1d3b7-25eb-4ac8-81ed-ad740fd1a297"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x7f1873f28e60>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zycxUz32/lAiXmx2ozQPFlrIlyB0l2v7zzz9n/vz5DB8+nLFjx3L27FleffXV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WraJNm9KLA7k5DhH14bOsZ9Y4koR5tYWoOxJF1K9fvw7cSlcq2iLVniiFNJSykOqWjNaC4fLy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\nAoGHIERdIBAIBAIPQYi6QCAQCAQewv8DVmyPG2w+cmwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f187408ef10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=mpl.cm.coolwarm,\n",
    "        linewidth=0.5, antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: opt_plot_3d\n",
    "# title: Function to minimize with two parameters\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "uuid": "72b2e44d-2127-412e-9046-2b0c7c5bf7c6"
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as spo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "uuid": "e6c829bb-f358-430d-9e8c-781e9d15c9e6"
   },
   "outputs": [],
   "source": [
    "def fo((x, y)):\n",
    "    z = np.sin(x) + 0.05 * x ** 2 + np.sin(y) + 0.05 * y ** 2\n",
    "    if output == True:\n",
    "        print '%8.4f %8.4f %8.4f' % (x, y, z)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "uuid": "d1f54d32-6cb5-4cd2-8a95-ea3b92c87266"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-10.0000 -10.0000  11.0880\n",
      "-10.0000 -10.0000  11.0880\n",
      "-10.0000  -5.0000   7.7529\n",
      "-10.0000   0.0000   5.5440\n",
      "-10.0000   5.0000   5.8351\n",
      "-10.0000  10.0000  10.0000\n",
      " -5.0000 -10.0000   7.7529\n",
      " -5.0000  -5.0000   4.4178\n",
      " -5.0000   0.0000   2.2089\n",
      " -5.0000   5.0000   2.5000\n",
      " -5.0000  10.0000   6.6649\n",
      "  0.0000 -10.0000   5.5440\n",
      "  0.0000  -5.0000   2.2089\n",
      "  0.0000   0.0000   0.0000\n",
      "  0.0000   5.0000   0.2911\n",
      "  0.0000  10.0000   4.4560\n",
      "  5.0000 -10.0000   5.8351\n",
      "  5.0000  -5.0000   2.5000\n",
      "  5.0000   0.0000   0.2911\n",
      "  5.0000   5.0000   0.5822\n",
      "  5.0000  10.0000   4.7471\n",
      " 10.0000 -10.0000  10.0000\n",
      " 10.0000  -5.0000   6.6649\n",
      " 10.0000   0.0000   4.4560\n",
      " 10.0000   5.0000   4.7471\n",
      " 10.0000  10.0000   8.9120\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "spo.brute(fo, ((-10, 10.1, 5), (-10, 10.1, 5)), finish=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "uuid": "dc42167b-4e8f-462c-8aad-a94afdf0a8bc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.4, -1.4])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "opt1 = spo.brute(fo, ((-10, 10.1, 0.1), (-10, 10.1, 0.1)), finish=None)\n",
    "opt1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "uuid": "ec2669cd-36a5-4b79-a90c-761a39b12044"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7748994599769203"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "uuid": "e451a278-e2ae-4d86-b357-f230468052a4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " -1.4000  -1.4000  -1.7749\n",
      " -1.4700  -1.4000  -1.7743\n",
      " -1.4000  -1.4700  -1.7743\n",
      " -1.3300  -1.4700  -1.7696\n",
      " -1.4350  -1.4175  -1.7756\n",
      " -1.4350  -1.3475  -1.7722\n",
      " -1.4088  -1.4394  -1.7755\n",
      " -1.4438  -1.4569  -1.7751\n",
      " -1.4328  -1.4427  -1.7756\n",
      " -1.4591  -1.4208  -1.7752\n",
      " -1.4213  -1.4347  -1.7757\n",
      " -1.4235  -1.4096  -1.7755\n",
      " -1.4305  -1.4344  -1.7757\n",
      " -1.4168  -1.4516  -1.7753\n",
      " -1.4305  -1.4260  -1.7757\n",
      " -1.4396  -1.4257  -1.7756\n",
      " -1.4259  -1.4325  -1.7757\n",
      " -1.4259  -1.4241  -1.7757\n",
      " -1.4304  -1.4177  -1.7757\n",
      " -1.4270  -1.4288  -1.7757\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-1.42702972, -1.42876755])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "opt2 = spo.fmin(fo, opt1, xtol=0.001, ftol=0.001, maxiter=15, maxfun=20)\n",
    "opt2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "uuid": "0352d556-6ea7-47a6-9c76-e4a56c0efed7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7757246992239009"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "uuid": "ff9beaf9-73d7-4157-85cb-24783abae775"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.015826\n",
      "         Iterations: 46\n",
      "         Function evaluations: 86\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 4.2710728 ,  4.27106945])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "spo.fmin(fo, (2.0, 2.0), maxiter=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constrained Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "# function to be minimized\n",
    "from math import sqrt\n",
    "def Eu((s, b)):\n",
    "    return -(0.5 * sqrt(s * 15 + b * 5) + 0.5 * sqrt(s * 5 + b * 12))\n",
    "\n",
    "# constraints\n",
    "cons = ({'type': 'ineq', 'fun': lambda (s, b):  100 - s * 10 - b * 10})\n",
    "  # budget constraint\n",
    "bnds = ((0, 1000), (0, 1000))  # uppper bounds large enough"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "uuid": "8f989832-637a-4188-b096-26ceeabd77ea"
   },
   "outputs": [],
   "source": [
    "result = spo.minimize(Eu, [5, 5], method='SLSQP',\n",
    "                       bounds=bnds, constraints=cons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "uuid": "67c11995-124c-4f9d-8edf-1364b412e754"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  status: 0\n",
       " success: True\n",
       "    njev: 5\n",
       "    nfev: 21\n",
       "     fun: -9.700883611487832\n",
       "       x: array([ 8.02547122,  1.97452878])\n",
       " message: 'Optimization terminated successfully.'\n",
       "     jac: array([-0.48508096, -0.48489535,  0.        ])\n",
       "     nit: 5"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "uuid": "53899a89-8532-4f22-a17f-54d106412867"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.02547122,  1.97452878])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "uuid": "b8548809-fe3a-4fa4-9496-8d3b6a177973"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.700883611487832"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-result['fun']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "uuid": "7453e87b-a70d-47b9-8a12-c5c0f01e4b86"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.999999999999986"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(result['x'], [10, 10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "uuid": "6a38567d-4a2d-464f-8de3-7687e1d2916d"
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as sci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "uuid": "0954e5b6-9874-4bad-a2fb-28273a015e4a"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "uuid": "afb6151f-5743-4950-980e-18047e066ebc"
   },
   "outputs": [],
   "source": [
    "a = 0.5  # left integral limit\n",
    "b = 9.5  # right integral limit\n",
    "x = np.linspace(0, 10)\n",
    "y = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "uuid": "ad78923f-e4c1-4381-9a24-33b4f1ea3c56"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.axis.YTick at 0x7f1873e62510>,\n",
       " <matplotlib.axis.YTick at 0x7f1873eb4690>]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dYMiQpep9KUelsBORqOX1Qp8+XgC6dVtJzZqa+1KOTmEnIlHrr38NsHp1EmedtZtu3bR0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\nU9iJiEjM+/9gJ7nIzh2mcwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1873fc3b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Polygon\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "plt.plot(x, y, 'b', linewidth=2)\n",
    "plt.ylim(ymin=0)\n",
    "\n",
    "# area under the function\n",
    "# between lower and upper limit\n",
    "Ix = np.linspace(a, b)\n",
    "Iy = f(Ix)\n",
    "verts = [(a, 0)] + list(zip(Ix, Iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='0.7', edgecolor='0.5')\n",
    "ax.add_patch(poly)\n",
    "\n",
    "# labels\n",
    "plt.text(0.75 * (a + b), 1.5, r\"$\\int_a^b f(x)dx$\",\n",
    "         horizontalalignment='center', fontsize=20)\n",
    "\n",
    "plt.figtext(0.9, 0.075, '$x$')\n",
    "plt.figtext(0.075, 0.9, '$f(x)$')\n",
    "\n",
    "ax.set_xticks((a, b))\n",
    "ax.set_xticklabels(('$a$', '$b$'))\n",
    "ax.set_yticks([f(a), f(b)])\n",
    "# tag: sin_integral\n",
    "# title: Example function with integral area\n",
    "# size: 50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "uuid": "6d3aa9c8-58c0-46a3-a89f-ca471a1f83e4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.366995967084602"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.fixed_quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "uuid": "0ddebba6-5357-4ce9-b829-d752132d12df"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086752"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "uuid": "3b1779d6-c831-449d-964f-e2cc869847e7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086713"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.romberg(f, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "uuid": "5499809d-f2b1-4cc9-8808-511f4e82c5ed"
   },
   "outputs": [],
   "source": [
    "xi = np.linspace(0.5, 9.5, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "uuid": "aec239bc-cdd9-4477-b47c-4d0136ed686d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.352733271544516"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.trapz(f(xi), xi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "uuid": "ce33e420-5143-4d54-b23f-0040f54723fc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374964184550748"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.simps(f(xi), xi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration by Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "uuid": "bb840eb2-0e13-40eb-aea7-0f106dcf9f41"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.8047622793\n",
      "26.5229188983\n",
      "26.2655475192\n",
      "26.0277033994\n",
      "24.9995418144\n",
      "23.8818101416\n",
      "23.5279122748\n",
      "23.507857659\n",
      "23.6723674607\n",
      "23.6794104161\n",
      "24.4244017079\n",
      "24.2390053468\n",
      "24.115396925\n",
      "24.4241919876\n",
      "23.9249330805\n",
      "24.1948421203\n",
      "24.1173483782\n",
      "24.1006909297\n",
      "23.7690510985\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 20):\n",
    "    np.random.seed(1000)\n",
    "    x = np.random.random(i * 10) * (b - a) + a\n",
    "    print np.sum(f(x)) / len(x) * (b - a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false,
    "uuid": "f01d358d-8094-426c-8e69-657218d8c319"
   },
   "outputs": [],
   "source": [
    "import sympy as sy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "uuid": "2cb7d5d8-ae45-4001-863e-714df216a656"
   },
   "outputs": [],
   "source": [
    "x = sy.Symbol('x')\n",
    "y = sy.Symbol('y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "uuid": "7bf55a76-f348-4820-af94-a83ed233d9a2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "uuid": "a8f0388b-1df6-4389-877c-af5d9f141708"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(x)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.sqrt(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "uuid": "f308fe2e-a5bc-4c88-a7f6-a4f09a568f2f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(x) - 13"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + sy.sqrt(x) - 4 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "uuid": "025f5084-4efc-4416-a564-b8a96ec426fd"
   },
   "outputs": [],
   "source": [
    "f = x ** 2 + 3 + 0.5 * x ** 2 + 3 / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false,
    "uuid": "f427581e-50ba-45b9-a145-ff734be26e59"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5*x**2 + 4"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.simplify(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "uuid": "59837e7c-a82f-44e5-8b87-b0fba310ffc5"
   },
   "outputs": [],
   "source": [
    "sy.init_printing(pretty_print=False, use_unicode=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "uuid": "ea1bbb85-a431-4e6c-a264-6ffb6df9f59e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     2    \n",
      "1.5*x  + 4\n"
     ]
    }
   ],
   "source": [
    "print sy.pretty(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "uuid": "e8702014-5347-4eac-b10c-39c5a54459c9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ___      \n",
      "\\/ x  + 0.5\n"
     ]
    }
   ],
   "source": [
    "print sy.pretty(sy.sqrt(x) + 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "uuid": "b8cf7cf4-56e2-4c6b-a70b-6592ec4bd6a6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.14159265358979323846264338327950288419'"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str = str(sy.N(sy.pi, 400000))\n",
    "pi_str[:40]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "uuid": "595cc15e-99b8-43c7-ad89-db4500fdb860"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'8245672736856312185020980470362464176198'"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str[-40:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "uuid": "cc4b85c4-e603-4d36-9553-f3999e877fca"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "366713"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str.find('111272')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "uuid": "c310eeab-ac04-4015-a327-29628f9a9a11"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false,
    "uuid": "60076f9d-93f3-47e0-b5b6-87d1bca3d30a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2, 2]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1 - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false,
    "uuid": "6c9e1060-61e6-4b18-9be4-cb71b83fc5a7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.858094329496553, -0.679047164748276 - 0.839206763026694*I, -0.679047164748276 + 0.839206763026694*I]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 3 + 0.5 * x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false,
    "uuid": "fcd70615-0db5-4c5c-8246-245ba3c8501c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: -I*y}, {x: I*y}]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 + y ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false,
    "uuid": "503329d1-812a-461c-9019-e6bb2a44125e"
   },
   "outputs": [],
   "source": [
    "a, b = sy.symbols('a b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false,
    "uuid": "af7bf980-d65b-4567-8576-404e79c5ac65"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  b                    \n",
      "  /                    \n",
      " |                     \n",
      " |  (0.5*x + sin(x)) dx\n",
      " |                     \n",
      "/                      \n",
      "a                      \n"
     ]
    }
   ],
   "source": [
    "print sy.pretty(sy.Integral(sy.sin(x) + 0.5 * x, (x, a, b)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false,
    "uuid": "89d4c980-01d7-423a-a2ab-a9698787019a"
   },
   "outputs": [],
   "source": [
    "int_func = sy.integrate(sy.sin(x) + 0.5 * x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false,
    "uuid": "38141163-7d29-4bd6-bfaf-9f9cfad86967"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      2         \n",
      "0.25*x  - cos(x)\n"
     ]
    }
   ],
   "source": [
    "print sy.pretty(int_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false,
    "uuid": "51d4481a-c6b6-4caa-b4d1-aa6fb04d4493"
   },
   "outputs": [],
   "source": [
    "Fb = int_func.subs(x, 9.5).evalf()\n",
    "Fa = int_func.subs(x, 0.5).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false,
    "uuid": "0c46e097-c665-440e-9d05-03c0d6e6d8d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180867"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fb - Fa  # exact value of integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false,
    "uuid": "657b13dc-101e-4c0c-9d15-43dbd418c3c8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           2         2                  \n",
      "- - -0.25*a  + 0.25*b  + cos(a) - cos(b)\n"
     ]
    }
   ],
   "source": [
    "int_func_limits = sy.integrate(sy.sin(x) + 0.5 * x, (x, a, b))\n",
    "print sy.pretty(int_func_limits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false,
    "uuid": "5c65cea8-1e15-4efa-aba4-52888becaf19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180868"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func_limits.subs({a : 0.5, b : 9.5}).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false,
    "uuid": "b13767c8-4878-42c1-b738-0727b824b329"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180868"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.integrate(sy.sin(x) + 0.5 * x, (x, 0.5, 9.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false,
    "uuid": "6ea93bb3-eb7c-4837-8327-621f3752b657"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5*x + sin(x)"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func.diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false,
    "uuid": "164131fd-a197-40ce-85d6-94221e808073"
   },
   "outputs": [],
   "source": [
    "f = (sy.sin(x) + 0.05 * x ** 2\n",
    "   + sy.sin(y) + 0.05 * y ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false,
    "uuid": "5d1ce51b-2536-469b-b516-56db1e86519a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*x + cos(x)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_x = sy.diff(f, x)\n",
    "del_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false,
    "uuid": "8d778c21-ed6a-43f0-8347-b95af334972a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*y + cos(y)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_y = sy.diff(f, y)\n",
    "del_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false,
    "uuid": "588daaba-266a-43da-a4b9-baeb56fc1ac8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpf('-1.4275517787645941')"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, -1.5)\n",
    "xo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false,
    "uuid": "2ef9beca-58f2-470b-a50e-6292bffbf2e0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpf('-1.4275517787645941')"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, -1.5)\n",
    "yo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false,
    "uuid": "c0812b29-c69f-4a30-aaf1-1447d1434cf4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.77572565314742"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf() \n",
    "  # global minimum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false,
    "uuid": "fd89d904-eab3-4035-941a-785c6a3f36cb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpf('1.7463292822528528')"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, 1.5)\n",
    "xo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false,
    "uuid": "cc99d8f4-e062-4c7e-85ae-46e96d3c8f19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpf('1.7463292822528528')"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, 1.5)\n",
    "yo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false,
    "uuid": "54622abe-cef1-47ff-bf23-b883cf588a91"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.27423381055640"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf()\n",
    "  # local minimum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://www.pythonquants.com\" target=\"_blank\">www.pythonquants.com</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a>\n",
    "\n",
    "<a href=\"mailto:analytics@pythonquants.com\">analytics@pythonquants.com</a>\n",
    "\n",
    "**Python Quant Platform** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://www.derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://shop.oreilly.com/product/0636920032441.do\" target=\"_blank\">Python for Finance @ O'Reilly</a>"
   ]
  }
 ],
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